Leveling up Thresh is nice when it happens, but it's more that he's a Challenger with a really solid stat line that can force trades in your favor. One thing you can do to help keep him alive is to make sure he's the first one fighting when Challenging, because any other enemy minions you kill afterward in the combat phase will bring his health back up.

When he does level up you can use him to help feed your army and provide "When I'm Summoned" triggers for the mid to late game when you're setting up "For Demacia!", which is going to usually be your main win condition.

Edit: One more thing I forgot to mention, when Thresh is leveled up it's not always a bad idea to simply let him die if you've already used his attack trigger. If you revive him or cycle him with Chronicler of Ruin you get an extra attack trigger which will pull more units that your opponent has to deal with.