Following a Labour leader's side (7)
I believe the answer is:
lateral
'side' is the definition.
('lateral' can be a synonym of 'side')
'following a labour leader's' is the wordplay.
'following' becomes 'later' (I've seen this before**).
'leader's' says to take the initial letters (I've seen 'leaders' mean this).
The first letter of 'labour' is 'l'.
'later'+'a'+'l'='LATERAL'
(Other definitions for lateral that I've seen before include "Towards the side" , "Situated at or extending to the side" , "One type of thinking" , "Tall ear (anag.)" , "Sort of thinking" .)