Obstinate, not born to be a butt (4)
I believe the answer is:
stub
'a butt' is the definition.
(I know that butt can be written as stub)
'obstinate not born' is the wordplay.
'obstinate' becomes 'stubborn' (obstinate means firm or stubborn).
'not' is a deletion indicator.
'stubborn' with 'born' taken away is 'STUB'.
'to be' is the link.
(Other definitions for stub that I've seen before include "evidence of smoking, for example" , "Stump, of a cigarette say" , "Knock (e.g. toe)" , "Short remaining piece" , "Strike against hard object - one's toe, perhaps" .)