Collar hasn't a zip (3)
I believe the answer is:
nil
'zip' is the definition.
('nil' can be a synonym of 'zip')
'collar hasn't a' is the wordplay.
'collar' becomes 'nail' ('nail' can be a synonym of 'collar').
'hasn't' indicates named letters should be taken away.
'nail' with 'a' taken away is 'NIL'.
(Other definitions for nil that I've seen before include "There's nothing left" , "Nothing, no score" , "Nothing found in senility" , "Nothing, zero" , "0" .)