Embarrassed about own goal, a politician becomes offensive (10)
I believe the answer is:
derogatory
'offensive' is the definition.
(thesaurus)
'embarrassed about own goal a politician' is the wordplay.
'embarrassed' becomes 'red' (I've seen this before).
'about' shows that the letters should be reversed in order.
'own goal' becomes 'og' (football abbreviation).
'politician' becomes 'tory' (I've seen this before).
'red' reversed gives 'der'.
'der'+'og'+'a'+'tory'='DEROGATORY'
'becomes' is the link.
(Other definitions for derogatory that I've seen before include "Disparaging" , "deliberately offensive" , "Showing a disrespectful attitude" , "Insulting" .)