Dispute - it’s French, involving old religious books (7)
I believe the answer is:
contest
'dispute' is the definition.
(I've seen this in another clue)
'french involving old religious books' is the wordplay.
'french' becomes 'cest' (I can't justify this - if you can you should give a lot more credence to this answer).
'involving' indicates putting letters inside.
'old' becomes 'o' (abbreviation).
'religious books' becomes 'NT' (New Testament).
'o'+'nt'='ont'
'cest' placed around 'ont' is 'CONTEST'.
'it's' is the link.
Can you help me to learn more?
(Other definitions for contest that I've seen before include "Match" , "Competition; dispute" , "Oppose - competition" , "Competition or conflict" , "Tournament" .)