Beat the Parisian in the lead, lapping gutless runner (6)
I believe the answer is:
larrup
'beat' is the definition.
(I know that larrup is a more specific form of beat)
'the parisian in the lead lapping gutless runner' is the wordplay.
'the parisian' becomes 'la' (French for the).
'in the lead' becomes 'up' (similar in meaning).
'lapping' is an insertion indicator (lapping can mean covering or wrapping).
'gutless' suggests removing the centre.
'runner' with its middle removed is 'rr'.
'la'+'up'='laup'
'laup' going around 'rr' is 'LARRUP'.
(Other definitions for larrup that I've seen before include "Flog" , "Hit hard" .)