Offensive old goat misbehaving in part of Ulster (10)
I believe the answer is:
derogatory
'offensive' is the definition.
(I've seen this before)
'old goat misbehaving in part of ulster' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'misbehaving' is an anagram indicator.
'in' is an insertion indicator.
'part of ulster' becomes 'derry' (Derry is a city in Ulster).
'o'+'goat'='ogoat'
'ogoat' with letters rearranged gives 'ogato'.
'ogato' inserted within 'derry' is 'DEROGATORY'.
(Other definitions for derogatory that I've seen before include "Showing a disrespectful attitude" , "deliberately offensive" , "Disparaging" , "Insulting" .)