Rooney's caught Peter out (4)
I believe the answer is:
wane
'peter out' is the definition.
(thesaurus)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for wane that I've seen before include "Diminish" , "Decrease, decline" , "Decrease in size or power" , "Atrophy" , "Lose force, intensity" .)