Wrap about finished (5)
I believe the answer is:
cover
'wrap' is the definition.
(I know that wrap is a more specific form of the action cover)
'about finished' is the wordplay.
'about' becomes 'c' (abbreviation for circa).
'finished' becomes 'over' (over can mean finished or ended).
'c'+'over'='COVER'
(Other definitions for cover that I've seen before include "Fielder" , "Totally obscure" , "Shroud" , "Sit on - suffice for" , "Deal with" .)