Animosity engendered by lie involving Republican (8)
I believe the answer is:
friction
'animosity' is the definition.
(I've seen this before)
'lie involving republican' is the wordplay.
'lie' becomes 'fiction' (I've seen this before).
'involving' indicates putting letters inside.
'republican' becomes 'R' (abbreviation in US politics).
'fiction' enclosing 'r' is 'FRICTION'.
'engendered by' is the link.
(Other definitions for friction that I've seen before include "State of conflict, clash" , "The rubbing of one object against another" , "Sliding resistance" , "bad blood" , "Retarding factor - discord" .)