Discover a smear about Church rector (9)
I believe the answer is:
ascertain
'discover' is the definition.
(ascertaining is a kind of discovering)
'a smear about church rector' is the wordplay.
'smear' becomes 'stain' ('stain' can be a synonym of 'smear'**).
'about' means one lot of letters goes inside another.
'church' becomes 'ce' (abbreviation for Church of England).
'rector' becomes 'r'.
'ce'+'r'='cer'
'stain' going around 'cer' is 'scertain'.
'a'+'scertain'='ASCERTAIN'
(Other definitions for ascertain that I've seen before include "Get to know" , "Prove" , "Establish, find out" , "Become aware" , "settle" .)