Lean towards popular Conservative policy (7)
I believe the answer is:
incline
'lean towards' is the definition.
(thesaurus)
'popular conservative policy' is the wordplay.
'popular' becomes 'in'.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'policy' becomes 'line' (I've seen this before).
'in'+'c'+'line'='INCLINE'
(Other definitions for incline that I've seen before include "Have tendency or slope" , "lean forward" , "List" , "Lean (towards)" , "tip" .)