Bill has no time for problem (5)
I believe the answer is:
poser
'for problem' is the definition.
(poser is a kind of problem)
'bill has no time' is the wordplay.
'bill' becomes 'poster' (synonyms).
'has no' indicates named letters should be taken away.
'time' becomes 't' (abbreviation).
'poster' with 't' taken away is 'POSER'.
(Other definitions for poser that I've seen before include "Someone behaving so as to be noticed" , "subject for an artist?" , "Question; one trying to impress" , "Maybe model" , "Artist's model" .)