Conservative's ignoring Republican trifles (4)
I believe the answer is:
toys
'trifles' is the definition.
(I've seen this in another clue)
'conservative's ignoring republican' is the wordplay.
'conservative's' becomes 'tory's' (informal term for a Conservative Party member).
'ignoring' indicates named letters should be taken away.
'republican' becomes 'R' (abbreviation in US politics).
'torys' with 'r' taken out is 'TOYS'.
(Other definitions for toys that I've seen before include "Amusing items" , "Fiddles" , "dolls, for example" , "Chihuahuas?" , "Matters of no importance" .)