Basically, Alex grows up. He gets a cushy government job in (IIRC) a music archive as compensation for what was done to him.
He does try to do the whole gang thing on the side again, but this time around, he's much older than the other members - what amuses them bores him, the way they throw around money annoys him (now that he actually works for a living - cushy job or not), and staying up all night when you actually have to show up for work the next day isn't quite as appealing.
A few things happen that reinforce his perception that what he's playing at is pointless, including a meeting with one of his old gang buddies, now happily married and very respectably middle-class - and he basically decides that he's done with the things he did as a kid, and it's time to move on. Very similar to the ending of Trainspotting in some ways - "You think we're so different? Well, from now on, I'm going to be just like you. Job, wife, family. How do you like that?"