Religious establishment accommodating Italian will get precedence (8)
I believe the answer is:
priority
'precedence' is the definition.
('priority' can be a synonym of 'precedence')
'religious establishment accommodating italian' is the wordplay.
'religious establishment' becomes 'priory' (I've seen this before).
'accommodating' means one lot of letters goes inside another.
'italian' becomes 'it'.
'priory' going around 'it' is 'PRIORITY'.
'will get' is the link.
(Other definitions for priority that I've seen before include "the most important thing" , "Status establishing relative importance or urgency" , "Most urgent matter" , "Something regarded as more important than others" , "The right to go first" .)