Alien chasing British religious figure (7)
I believe the answer is:
brother
'religious figure' is the definition.
(title for a monk)
'alien chasing british' is the wordplay.
'alien' becomes 'other' (other can mean alien or unusual).
'chasing' means one lot of letters go next to another.
'british' becomes 'br' (abbreviation for British).
'other' put after 'br' is 'BROTHER'.
(Other definitions for brother that I've seen before include "Male sibling" , "Relation" , "Eg, monk, friar" , "Fellow-member" , "Union member - male relative" .)