Following a line sideways (7)
I believe the answer is:
lateral
'sideways' is the definition.
(thesaurus)
'following a line' is the wordplay.
'following' becomes 'later' (I've seen this before).
'line' becomes 'l'.
'later'+'a'+'l'='LATERAL'
(Other definitions for lateral that I've seen before include "Way of thinking" , "Possibly right" , "Side branch" , "This kind of sideways thinking does not use conventional logic" , "Relating to the side" .)