Influence behind admitting Further Education college's principal (6)
I believe the answer is:
affect
'influence' is the definition.
(I've seen this before)
'behind admitting further education college's principal' is the wordplay.
'behind' becomes 'aft' (aft means towards or at the end of a ship).
'admitting' means one lot of letters goes inside another (admit can mean to welcome in or accept).
'principal' suggests taking the first letters.
The first letters of 'further education colleges' is 'fec'.
'aft' going around 'fec' is 'AFFECT'.
(Other definitions for affect that I've seen before include "Assume" , "Have impact upon" , "Arouse sadness or sympathy like tear-jerker" , "Act upon" , "Put on" .)