Degenerate duke to lie back, topless (7)
I believe the answer is:
decline
'degenerate' is the definition.
(I know this)
'duke to lie back topless' is the wordplay.
'duke' becomes 'd' (abbreviation).
'to lie back' becomes 'recline' (I've seen this before).
'topless' means to remove the first letter.
'recline' with its initial letter taken off is 'ecline'.
'd'+'ecline'='DECLINE'
(Other definitions for decline that I've seen before include "perform grammatical exercise" , "Refuse - to take a drop" , "Refuse; decay" , "Refuse to accept" , "Start to fail" .)