A few things I'd like to discuss. I've played this game for way too long, and over the course of my time in the community, I've tried every off-meta and flavor of the month jungler that has ever come into existence. There have been times where mid-late game junglers were ridiculously strong and just afk-farming was the strat (see feral flare), but nowadays the strategy has changed. Make no mistake that I am telling you the truth when I say that every good/meta jungler, and I mean EVERY SINGLE ONE, has a very high impact on the early game. Those that don't are very easily crippled without a good team supporting them. The way jungle XP and pathing works make it so that people who can level 2 gank or invade have such an edge over those that can't that it is near impossible to play late game junglers. Short answer, don't play late game junglers, especially NOT IN THIS META, if you want to climb fast.
Longer answer: To play a late-game jungler, you have to constantly be out macro-ing your opponent. You'll obviously be looking to power farm, but that doesn't mean you can't have ANY impact on the early stages of the game. If I'm ever playing a more mid-late game based jungler (e.g. Zac, Ivern, Fiddlesticks), I do my absolute best to always keep tabs on the enemy jungler. Is he pressuring bot? Maybe it's time for me to set up for a counter-gank. Is he camping top? Maybe I try to counter jungle or pressure drake for my team. What you'll really be looking to do is make it as hard as possible for the enemy to snowball by making him trade every kill, every turret, and every drake for something else. Hopefully, if you do this right, and get lucky that your team isn't inting too hard, then you'll be able to walk into a team fight late game and carry the whole damn thing.