Allows haircuts without sex appeal (7)
I believe the answer is:
permits
'allows' is the definition.
('permit' can be a synonym of 'allow')
'haircuts without sex appeal' is the wordplay.
'haircuts' becomes 'perms' (perm is a type of haircut).
'without' means one lot of letters goes inside another ('without' can be similar in meaning to 'outside').
'sex appeal' becomes 'it'.
'perms' placed around 'it' is 'PERMITS'.
(Other definitions for permits that I've seen before include "Allows" , "Consents to" .)