Former pupil’s story involving constant showjumping feature (8)
I believe the answer is:
obstacle
'showjumping feature' is the definition.
'former pupil's story involving constant' is the wordplay.
'former pupil's' becomes 'obs' (abbreviation for 'Old Boy').
'story' becomes 'tale' ('tale' can be a synonym of 'story').
'involving' is an insertion indicator.
'constant' becomes 'c' (mathematical abbreviation).
'tale' placed around 'c' is 'tacle'.
'obs'+'tacle'='OBSTACLE'
(Other definitions for obstacle that I've seen before include "It hinders or prevents advance" , "Maybe let" , "Blockage, hindrance" , "stumbling block" , "Stab Cleo (anag) - which hinders progress" .)