Old boy's story involves Conservative block (8)
I believe the answer is:
obstacle
'block' is the definition.
(an obstacle is a block or blockage)
'old boy's story involves conservative' is the wordplay.
'old boy's' becomes 'obs' (abbreviation for a private school 'old boy').
'story' becomes 'tale' (synonyms).
'involves' means one lot of letters goes inside another.
'conservative' becomes 'C' (UK political abbreviation).
'tale' enclosing 'c' is 'tacle'.
'obs'+'tacle'='OBSTACLE'
(Other definitions for obstacle that I've seen before include "Hurdle, impediment" , "It obstructs or hinders" , "hold-up" , "difficulty" , "Maybe let" .)