Obsolete seat, not entirely a Roman Catholic holding (7)
I believe the answer is:
archaic
'obsolete' is the definition.
(I know that obsolete can be written as archaic)
'a roman catholic holding' is the wordplay.
'roman' becomes 'chai' (I am not sure about this - if you are sure you should believe this answer much more).
'catholic' becomes 'RC' (Roman Catholic).
'holding' is an insertion indicator.
'chai' going within 'rc' is 'rchaic'.
'a'+'rchaic'='ARCHAIC'
'seat not entirely' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for archaic that I've seen before include "Of a much earlier period" , "Outdated" , "From the past" , "Antiquarian" , "Obsolete" .)