Hang about, initially investigating expensive underwear (8)
I believe the answer is:
lingerie
'underwear' is the definition.
(type of underwear)
'hang about initially investigating expensive' is the wordplay.
'hang about' becomes 'linger' (I've seen this before).
'initially' says to take the initial letters.
The first letters of 'investigating expensive' is 'ie'.
'linger'+'ie'='LINGERIE'
(Other definitions for lingerie that I've seen before include "Women's underclothes" , "flimsy stuff" , "Slinky undergarments" , "Female underwear" , "stockings, say?" .)