Not so many head off with this vessel (4)
I believe the answer is:
ewer
'this vessel' is the definition.
(ewer is a type of jug)
'not so many head off' is the wordplay.
'not so many' becomes 'fewer' ('few' can be the opposite of 'many' so perhaps 'fewer' is reasonable for 'not so many').
'head off' means to remove the first letter (the first letter or 'head' is removed).
'fewer' with its initial letter taken off is 'EWER'.
'with' is the link.
(Other definitions for ewer that I've seen before include "Jar for water" , "Jug with wide spout" , "water-carrier" , "Large water-jug" , "Large water jug" .)