Tack supplier’s son finally fell, bitten by snake (7)
I believe the answer is:
saddler
'tack supplier's' is the definition.
(tack is horse-riding gear)
'son finally fell bitten by snake' is the wordplay.
'son' becomes 's'.
'finally' suggests the final letters.
'bitten by' is an insertion indicator (I've seen this in other clues).
'snake' becomes 'adder' (adder is a kind of snake).
The last letter of 'fell' is 'l'.
'l' put into 'adder' is 'addler'.
's'+'addler'='SADDLER'
(Other definitions for saddler that I've seen before include "Maker of horse's equipment" , "I'll make seat" , "One makes leather goods for horses" , "he'll offer you a seat" , "Leather-worker" .)