Experienced in non-believer's education (6)
I believe the answer is:
versed
'experienced' is the definition.
(I've seen this in another clue)
'in non-believer's education' is the wordplay.
'in' indicates the answer is hidden within the clue.
'VERSED' can be found hidden inside 'non believers education'.
(Other definitions for versed that I've seen before include "Thoroughly acquainted with and skilled in something" , "Thoroughly acquainted with - served (anag)" , "Experienced or skilled in" , "Having knowledge, skilled - in poetry?" , "Well-informed" .)