Obstinacy recanting sin about embracing sweetheart (13)
I believe the answer is:
intransigence
'obstinacy' is the definition.
(intransigence is a kind of obstinacy)
'recanting sin about embracing sweetheart' is the wordplay.
'about' indicates anagramming the letters.
'embracing' means one lot of letters goes inside another.
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'recanting'+'sin'='recantingsin'
'recantingsin' anagrammed gives 'intransignce'.
'intransignce' enclosing 'e' is 'INTRANSIGENCE'.
(Other definitions for intransigence that I've seen before include "Refusal to compromise or discuss" , "Obstinacy" , "Stubbornness" , "uncompromising attitude" , "Refusal to change one's views" .)