Very quick to go topless, being tasteless (5)
I believe the answer is:
vapid
'tasteless' is the definition.
(I've seen this in another clue)
'very quick to go topless' is the wordplay.
'very' becomes 'v' (common abbreviation).
'quick' becomes 'rapid' (synonyms).
'to go topless' means to remove the first letter.
'rapid' with its initial letter removed is 'apid'.
'v'+'apid'='VAPID'
'being' acts as a link.
(Other definitions for vapid that I've seen before include "Insipid - lacking significance" , "Wishy-washy" , "Insipid or uninteresting" , "Boring or lifeless" , "Insipid, empty" .)