Act wildly — drop one’s capital cover? (3,4,4,4)
I believe the answer is:
let ones hair down
'act wildly' is the definition.
'drop one's capital cover?' is the wordplay.
I cannot quite see how this works, but
'one's' could be 'ones' and 'ones' is found within the answer.
'capital' could be 'ai' and 'ai' is located in the answer.
This explanation may well be incorrect...
(Other definitions for let ones hair down that I've seen before include "lowering the shock level" , "act without reserve" , "have a lot of fun" , "party" , "Be a disgrace to Barnet" .)