Backing some officials but not of the clergy (4)
I believe the answer is:
laic
'not of the clergy' is the definition.
'backing some officials but' is the wordplay.
'backing' says the letters should be written in reverse.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'cial' can be found hidden inside 'officials but'.
'cial' reversed gives 'LAIC'.
(Other definitions for laic that I've seen before include "Non-clergy" , "Of those not members of the clergy" , "people not in church" , "belonging to the people" , "Of non-clerical people" .)