Religious rite gets agreement out of court (7)
I believe the answer is:
unction
'religious rite' is the definition.
'agreement out of court' is the wordplay.
'agreement' becomes 'union' (I've seen this before**).
'out of' means one lot of letters goes inside another.
'court' becomes 'ct'.
'union' placed around 'ct' is 'UNCTION'.
'gets' is the link.
(Other definitions for unction that I've seen before include "Affected charm" , "Ointment - (false?) sincerity" , "Oiliness" , "Excessive politeness" , "Smarminess" .)