Go after a cash prize out of turn (6)
I believe the answer is:
pursue
'go after' is the definition.
(synonyms)
'a cash prize out of turn' is the wordplay.
'a cash prize' becomes 'purse' (I've seen this before).
'out of' means one lot of letters goes inside another (some letters on the outside of others).
'turn' becomes 'U' (a 'U-turn' is a kind of turn).
'purse' enclosing 'u' is 'PURSUE'.
(Other definitions for pursue that I've seen before include "Follow, chase" , "Seek" , "Give chase" , "Be engaged in - hunt" , "Try to win" .)