Following a Labour leader on the side (7)
I believe the answer is:
lateral
'on the side' is the definition.
(I've seen this before)
'following a labour leader' is the wordplay.
'following' becomes 'later' (I've seen this before**).
'leader' suggests taking the first letters.
The initial letter of 'labour' is 'l'.
'later'+'a'+'l'='LATERAL'
(Other definitions for lateral that I've seen before include "Towards the side" , "Relating to the side" , "Tall ear (anag.)" , "Situated at or extending to the side" , "Sidelong" .)