Regretting wearing hairpiece to go outside (5)
I believe the answer is:
ruing
'regretting' is the definition.
('rue' can be a synonym of 'regret')
'wearing hairpiece to go outside' is the wordplay.
'wearing' becomes 'in' (as in being 'in' certain clothes).
'hairpiece' becomes 'rug' (rug is a kind of hairpiece).
'to go outside' is an insertion indicator.
'in' going inside 'rug' is 'RUING'.
(Other definitions for ruing that I've seen before include "Having second thoughts" , "Feeling sorry for" , "Regretful" , "Feeling bad" , "feeling remorse" .)