Thresh is THE mobility support. Many people used to get a tanky champion but if you're focused (arrive when you engage) you'll burn in 3 seconds and loose your aegis effect. Then, let's go to talk about Thresh AP support.

First, use the abilitie power's quints because your AP.
Two, armor and scaling magic resistance must never change on any rune pages and champions.
Three, attack damage increase your E passive because you make 200% of it in additional magic damage.

At start, take the Targon if you know how to play thresh. I buy items in this order but if you're loosing, aegis first. Else zeke is very good for your ADC but very difficult to use, so be careful with that. You can also give the buff to your APC, that's work too ;) The censer is the master piece of your lanthern. attack speed and magic damage on hit increase just on the launch of the W on allies can change a team fight in your own.

On early, farm souls and harass the ennemies are the key to win. Don't forget, your Q stun ennemies, that's a good spell for harass and prevent the ennemies who farm or need to heal ( like alistar). But don't jump if that can't give a kill.

On midgame, grab with A, let the lanthern on your back for the jungler or the top, PRESS R, and if they're fleeing, use E on your back for slow them...again.

On Lategame, you're a blood beast who have near than 150 stacks, so 112.5 AP and armor passively. (0.75 per stacks). Have a nice day with the best mobility support. And don't KS with him. 1 kill is good, 2 is a waste.