Several refuse to admit Conservative leaning (8)
I believe the answer is:
tendency
'leaning' is the definition.
('tendency' can be a synonym of 'leaning')
'several refuse to admit conservative' is the wordplay.
'several' becomes 'ten' (I've seen this in other clues).
'refuse' becomes 'deny' ('deny' can be a synonym of 'refuse'**).
'to admit' indicates putting letters inside.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'deny' enclosing 'c' is 'dency'.
'ten'+'dency'='TENDENCY'
(Other definitions for tendency that I've seen before include "Political group" , "Inclination - political faction" , "movement" , "Inclination or leaning" , "Inclination or trend" .)