Vow is old hat, possibly (4)
I believe the answer is:
oath
'vow' is the definition.
('oath' can be a synonym of 'vow')
'old hat possibly' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'possibly' indicates anagramming the letters.
'hat' is an anagram of 'ath'.
'o'+'ath'='OATH'
'is' is the link.
(Other definitions for oath that I've seen before include "A word with a witness" , "Imprecation" , "bad language" , "A curse - or a pledge" , "Sworn promise" .)