Senior politician, Independent, entering cathedral (8)
I believe the answer is:
minister
'senior politician' is the definition.
(eg cabinet minister)
'independent entering cathedral' is the wordplay.
'independent' becomes 'i'.
'entering' is an insertion indicator.
'cathedral' becomes 'minster' (minster is a kind of cathedral).
'i' going within 'minster' is 'MINISTER'.
(Other definitions for minister that I've seen before include "Clergyman - politician" , "Senior politician" , "Member of parliament" , "Merit sin (anag.)" , "Member of government or clergy" .)