So Rek'Sai has been my main since her release, she's the most beautiful girl on the internet that I ever laid eyes upon.
Firstly, the main reason why she isn't part of the Tank rework is she was considered a Bruiser/Fighter/Diver more so than a Tank. Over the years the meta has shifted and they nerfed Rek'Sai into oblivion, so the poor Xer'Sai was forced into a more Tanky role of a Vanguard. This is why she generally builds a Titanic Hydra as her only damage item, as between the nerfs to her Armor, Health Growth, etc. she has been bullied into a more utility role of a front-line beefcake and builds a ton of Health to supplement that.
She does what she does EXTREMELY well - staying alive in the jungle. Her early clear isn't exactly the same as, say, Shyvana where the jungle creeps tend to bow down before you and die with relative ease, however with her Passive she remains VERY healthy when cleared properly. I'd recommend starting Raptors -> Red -> Wolves -> Blue -> Gromp for the fastest level 4 you can get, as with her AoE damage she fairs much better than most others. She also gains Fury based on the amount of enemies hit with her Unburrowed Q (Queen's Wrath), so it's incredibly easy to max out your Fury and gain the True Damage as well as bonus Healing from your Passive.
A nice Quality of Life of Rek'Sai is her ability to utilize her Passive while clearing. Generally, on your first clear or so, you'll start a camp with your Burrowed Q (Prey Seeker) and follow up with an immediate knock up with your Unburrow (W). This gives you ~100 damage for free to the jungle camps without any chance of retaliation from them. Use your Unburrowed Q to reset your Auto-Attack as well. Your E does more damage based on the amount of Fury Rek'Sai currently has, however saving it when you desperately need the early damage isn't always viable. You'll find that the healthiest way to clear the jungle is to use your Queen's Wrath twice, which syncs up well with your Unburrow and Prey Seeker, then follow it up with the same Prey Seeker -> Unburrow combo you started with, as the target with time out at nearly the perfect time to be knocked up again. This allows you to gain some Health back from your Passive, and prevents you from wasting precious Fury generation if you're already topped off. It rapidly decays when out of combat, so it's not the best idea to sit with full Fury and half Health. If you're not doing it already, utilize Attack Move as best as you can, walking away after taking a swipe at the enemy monsters and preventing yourself from getting hit during your downtime between attacks. This will almost guaranteed save you an entire jungle camp when done properly with almost any jungler.
For helping yourself out when clearing, you'll want to pick up an early Tiamat when you have 1200 gold. This is almost always the first item for Rek'Sai, as it supplements her clearing VERY well, being able to clear with the best of them at that point. It also functions as an auto-attack reset. Try it out in Practice Tool to get the hang of it, you're able to provide an immense amount of unexpected burst if you Queen's Wrath -> Tiamat immediately on a knocked up target. Most laners are simply unable to cope with her burst early game like that.
She starts falling off if the enemy team is ahead of yours. She's a vicious beast, but requires more Health/Armor/Magic Resistance than, say, a Nautilus does to stay alive. She's also extremely cunning in the respect of being able to create a massive network of tunnels that would otherwise make some terrain impossible to pass without a Flash being burnt. This is why she's very powerful in the right hands, as she can make the enemy jungler's life a living hell with a small advantage. Her Tremor Sense and Tunnels make her one of the safest counter-junglers in the game, as well as providing semi-safe protection against Evelynn, Twitch, and other stealth-based champions. She's also remarkably talented against Lee Sin, as you can deny his execute on his second Q with your Unburrow.
If she's ahead, she tends to stay ahead and close games out at a moderate pace. She's a farming machine and won't hesitate to clear the entire enemy's jungle, head back to base, clear hers, and repeat the process over and over again to continue pushing the enemy back into their base due to lack of safety. Dropping a few wards in the process will also protect your laners very well. She heavily relies upon having a team that can utilize her strengths, but will easily push the tempo on her own to help nudge them along.
A few tips for helping out a fellow Rek'Sai player:
-Keep a tunnel near your laners, in Mid lane you can often get away with placing one almost directly under the turret from the small bush near Wolves, however with Top and Bot lane you'll want to place them in the bush behind the lane where the enemy team won't step on it instantly to destroy it. This helps out with counter-ganks very well, and will send a smart enemy jungler running as they know you're down for a double/triple kill and will easily throw yourself into the fight.
-Her Flash -> W is nearly unavoidable, and with Courage of the Colossus she's a monster with some Health. Even your 0/10 Yasuo can be useful if you land that perfect multi-player knock up.
-She's very aggressive early, but don't make your appearance too well known to aggressive duelist-style junglers, as she doesn't out-duel a Kha'Zix or Lee Sin at level 3 without assistance.
-Although you don't want your appearance known by strong early junglers, you'll absolutely want to say "Hi." to the enemy laners. They often lack the tools to escape both yourself and your allied laner, and even with jungle assistance at that point your AA-reset + E will almost certainly push them out of lane and blow their Flash.
-Don't be scared to trade your Flash for the enemy laner's if you're confident you can make the kill happen. Rek'Sai excels in punishing lanes without mobility or Flash up, and can simply Tunnel into the enemy at that point. If they choose take a direct fight/knock up with you, it's certain death for them. If they choose to take the long route through their jungle, thank them for pathing you closer to their camps that you can take after.
-Your laners love you. You can give the first Blue Buff to your Mid laner if you trust them and want them to have some extra pressure. A Veigar, Orianna, Ahri, or Syndra with Blue at level 2 is a nightmare for the enemy team slinging out spells while they have no sustain compared to them at that point in the game.
-To emphasize the above point, you can also "gift" kills very easily to your team to further boost their morale. Rek'Sai will gladly camp a lane while constantly applying pressure to others with her Ultimate being ready, as she can appear anywhere at any time - faster than any Teleport can be channeled or seen. Although it's usually used as the term "Farm Alarm," if you utilize it a few times aggressively or to save a laner, the enemy team will often become extremely paranoid and insist on playing safe without their jungler being there for backup.
-Keep a healthy network of Tunnels on the map for yourself. It will help you immensely in clear speed, as well as provide a safety net to retreat into. Nobody feels good about Flashing over Dragon wall when Rek'Sai just Tunneled over only to take 3 more Tunnels and end up near mid/top lane. It's very infuriating to watch someone chase a talented Rek'Sai, as they will likely end up wasting their time and get collapsed upon by the enemy team.
-Your Tunnels help immensely with keeping both you and your team safe. Keep an eye on the minimap and watch if one randomly disappears (if it's not being timed out, of course). This is a guarantee that an enemy champion is destroying them and at that location currently, and you can MIA Ping for your team or prepare for the counter-gank.
-She will still get shredded by a 6-item ADC, that's the nature of the beast of this game to a degree. She brings a hardcore engage, however lacks disengage without her Tunnel (E) up. This is why you'll have to rely on your teammates, however as you climb you'll notice people tend to love what you do and won't hesitate to follow up on your engage. Rek'Sai is the only girl for Draven (as seen in the Pool Party lineup), so this should say something! :) Most enemy champions will be forced to disengage and use nearly every ability to peel Rek'Sai off while her team does work on the target you decided was not worthy of being on your screen.
-For ARAM/URF, try out AP'Sai if your team lacks AP and rush a Luden's Echo. Her AP Scaling is absolutely devastating as an artillery machine and very annoying to dodge every few seconds - like an AoE Nidalee Spear.
Hope this helps, I'd definitely recommend checking out the Rek'Sai Mains Reddit for some tips/tricks if you're interested. She's been nerfed to hell and back, but will always remain strong with her kit. She brings a primal and bestial sense to the table, and is one of the scariest champions around. That beautiful dorsal fin sends shivers down most laner's spine when the Land Shark makes a B-line for them, as killing her is extremely unlikely without great assistance, and surviving her is only a sliver of hope when she has her sights set on you. She makes every aspect of the game unsafe for the enemy team being able to appear from nowhere, and won't hesitate to Tower Dive you in a moment's notice.