Bill has no time for puzzle (5)
I believe the answer is:
poser
'puzzle' is the definition.
(I've seen this before)
'bill has no time' is the wordplay.
'bill' becomes 'poster' ('poster' can be a synonym of 'bill').
'has no' indicates named letters should be taken away.
'time' becomes 't'.
'poster' with 't' removed is 'POSER'.
'for' is the link.
(Other definitions for poser that I've seen before include "Puzzling question for the model" , "Puzzle using ropes" , "Ropes (anag.)" , "Tricky problem" , "Person still being portrayed" .)