I'd like to know the meaning of the idiom 'to carve the rush'.
I have just realised that you meant 'crave' and not 'carve'. However, I don't think this is an idiom.
This use of 'rush' is an abbreviated form of Adrenaline Rush - Wikipedia, the free encyclopedia. People who 'crave the rush' do things like bungee-jumping - triggering their fight-or-flight response just for fun. It's not an idiomatic phrase, but it's beginning to be used more widely.