You're early game will be rough for clearing so be sure to gank frequently to get your cinderhulk to make clearing easier. Also, Be sure to start Blue side, with a good leash you should be able to clear gromp/blue. If you could storm through early game without falling behind the rest of the game will be great.

Be sure to use your E on the enemy while ganking to make it easier for you to land your clocks to apply the stun. Your QWQ combo can be difficult to land sometimes but is very rewarding if landed. Practice makes Perfect.

Zilean jungle kind of falls off around the 15-20 minute mark. This is right before Zilean starts to get tanky so in team fights between 15-20 dont be a main front line, just land QWQ stuns and wait for the perfect ultimate on a carry.

Be sure to ult either your adc/apc or top carry if they are playing a damage top. NEVER ULT A TANK OR SUPPORT IN A TEAM FIGHT!

You will be going full tank so you become more of a front line opposed to full utility.
Having a Zilean could win a team fight so play smart, With a full tank Zilean you won't die much late game so if possible try and make the games go as long as possible to let Zilean scale and become the Tanky monster that he could be.

If you put in practice with Zilean JG all the elo and MMR could be yours. Have fun on the rift summoners and you can thank me later once you get to the Challenger Tier.