State of a house on the borders of Ireland (5)
I believe the answer is:
idaho
'state' is the definition.
(Idaho is an example)
'a house on the borders of ireland' is the wordplay.
'house' becomes 'ho' (abbreviation for house**).
'on' means one lot of letters go next to another.
'the borders of' means to remove the middle letters.
'ireland' with its middle removed is 'id'.
'a'+'ho'='aho'
'aho' put after 'id' is 'IDAHO'.
'of' acts as a link.
(Other definitions for idaho that I've seen before include "US state E. of Oregon" , "Pertaining to the Bard" , "O, I had a change in this state" , "State of northwest US" , "US state bordering Canada" .)