Westerly parts of Ireland entered by priest regularly, up-country (8)
I believe the answer is:
interior
'up-country' is the definition.
(synonyms)
'westerly parts of ireland entered by' is the wordplay.
'westerly parts' becomes 'inter' (I can't explain this - if you can you should give a lot more credence to this answer).
'of' becomes 'o''.
'ireland' becomes 'ir' (abbreviation for Ireland).
'entered by' is an insertion indicator.
'o' placed inside 'ir' is 'ior'.
'inter'+'ior'='INTERIOR'
'priest regularly' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for interior that I've seen before include "Inner part" , "Land away from the coast" , "Heartland" , "Central area of a country" , "The inside of anything" .)