Vinegar, say, has right to be strong (5)
I believe the answer is:
acrid
'be strong' is the definition.
(thesaurus)
'vinegar say has right' is the wordplay.
'vinegar say' becomes 'acid' (vinegar is a kind of acid).
'has' is an insertion indicator.
'right' becomes 'r' (abbreviation).
'acid' going around 'r' is 'ACRID'.
'to' is the link.
(Other definitions for acrid that I've seen before include "Strong and sharp" , "Unpleasantly bitter" , "Painfully pungent" , "Bitter in smell, like smoke" , "Pungent; caustic" .)