Next Labour leader taking a side (7)
I believe the answer is:
lateral
'side' is the definition.
('lateral' can be a synonym of 'side')
'next labour leader taking a' is the wordplay.
'next' becomes 'later' (I've seen this in other clues).
'leader' suggests taking the first letters.
'taking' indicates putting letters inside.
The first letter of 'labour' is 'l'.
'later'+'l'='laterl'
'laterl' enclosing 'a' is 'LATERAL'.
(Other definitions for lateral that I've seen before include "Towards the side" , "Edgeways" , "Side branch" , "Situated at or extending to the side" , "One type of thinking" .)