School subject, possibly thematic, includes religious instruction (10)
I believe the answer is:
arithmetic
'school subject' is the definition.
(I've seen this before)
'possibly thematic includes religious instruction' is the wordplay.
'possibly' indicates anagramming the letters.
'includes' is an insertion indicator.
'religious instruction' becomes 'ri' (abbreviation).
'thematic' with letters rearranged gives 'athmetic'.
'athmetic' enclosing 'ri' is 'ARITHMETIC'.
(Other definitions for arithmetic that I've seen before include "Calculation" , "Calculating" , "One of the three R's" , "Branch of maths" , "Numerical maths" .)