Aggravated, hate large dogs fighting (2,11)
I believe the answer is:
at loggerheads
'aggravated' is the definition.
(at loggerheads means in conflict)
'hate large dogs fighting' is the wordplay.
'fighting' is an anagram indicator (I've seen this in other clues).
'hate'+'large'+'dogs'='hatelargedogs'
'hatelargedogs' is an anagram of 'AT LOGGERHEADS'.
(Other definitions for at loggerheads that I've seen before include "In violent disagreement" , "In violent dispute" , "Quarrelling" , "Disagreeing with" , "In confrontation" .)