Become established in a Yorkshire town and an Ulster county (6,4)
I believe the answer is:
settle down
'become established' is the definition.
(synonyms)
'yorkshire town and an ulster county' is the wordplay.
'yorkshire town' becomes 'Settle' (Settle is a town in North Yorkshire).
'and' says to put letters next to each other.
'an ulster county' becomes 'Down' (County Down in Northern Ireland).
'settle'+'down'='SETTLE DOWN'
'in a' acts as a link.
(Other definitions for settle down that I've seen before include "Become quiet and orderly" , "put down roots" .)