Permissive swinger will leave a bill unpaid (8)
I believe the answer is:
allowing
'permissive' is the definition.
(I've seen this in another clue)
'swinger will leave a bill unpaid' is the wordplay.
'swinger' becomes 'bi' (bisexual, someone who 'swings both ways' sexually).
'will leave' suggests deleting specific letters.
'unpaid' becomes 'owing' (similar in meaning).
'a'+'bill'='abill'
'abill' with 'bi' taken away is 'all'.
'all'+'owing'='ALLOWING'
(Other definitions for allowing that I've seen before include "not stopping" , "Giving permission" , "Admitting" , "Permitting or conceding" , "Granting, permitting" .)