Initiation that's suitable is in British Museum (7)
I believe the answer is:
baptism
'initiation' is the definition.
(I know that baptism is a type of baptism)
'suitable is in british museum' is the wordplay.
'suitable' becomes 'apt' (apt means appropriate or fitting).
'in' is an insertion indicator.
'british museum' becomes 'bm'.
'apt'+'is'='aptis'
'aptis' placed inside 'bm' is 'BAPTISM'.
'that's' is the link.
(Other definitions for baptism that I've seen before include "Christening ceremony" , "Church admission rite" , "Religious ceremony" , "Religious rite involving water" , "Christian sacrament that symbolises admission to the church" .)