Inspire where the writer's Conservative, not Liberal (5)
I believe the answer is:
imbue
'inspire' is the definition.
(I've seen this before)
'the writer's conservative not liberal' is the wordplay.
'the writer's' becomes 'im' (both could mean 'the crossword setter is').
'conservative' becomes 'blue' (I've seen this before).
'not' suggests deleting specific letters.
'liberal' becomes 'l' (abbreviation).
'blue' with 'l' removed is 'bue'.
'im'+'bue'='IMBUE'
'where' is the link.
(Other definitions for imbue that I've seen before include "Suffuse with colour" , "Endow" , "Instil - soak" , "Fill with a feeling or quality" , "Suffuse - soak" .)