Lack of religious belief set him a problem (7)
I believe the answer is:
atheism
'lack of religious belief' is the definition.
'atheism' can be an answer for 'lack' (I have seen 'lack of faith' mean 'atheism' so perhaps 'lack' could also mean 'atheism'). I am not certain of the 'of religious belief' bit.
'set him a problem' is the wordplay.
'problem' is an anagram indicator.
'set'+'him'+'a'='sethima'
'sethima' anagrammed gives 'ATHEISM'.
Can you help me to learn more?
(Other definitions for atheism that I've seen before include "A lack of faith" , "Owed" , "Disbelief in gods" , "Lack of belief in the existence of God" , "displaying opposition to religion" .)