Quite a few cut off a late start (7)
I believe the answer is:
several
'quite a few' is the definition.
(I've seen this before)
'cut off a late start' is the wordplay.
'cut off' becomes 'sever' (to sever is to cut).
'start' indicates taking the first letters.
The first letter of 'late' is 'l'.
'sever'+'a'+'l'='SEVERAL'
(Other definitions for several that I've seen before include "Various, sundry" , "A few; separate" , "three or four" , "More than one or two" , "A good few" .)