Republican welcomed by dissident group in part (8)
I believe the answer is:
fraction
'part' is the definition.
(I know that fraction is a type of part)
'republican welcomed by dissident group' is the wordplay.
'republican' becomes 'R' (abbreviation in US politics).
'welcomed by' indicates putting letters inside (letters welcomed inside).
'dissident group' becomes 'faction'.
'r' going within 'faction' is 'FRACTION'.
'in' acts as a link.
(Other definitions for fraction that I've seen before include "Eg, an eighth" , "Inca fort (anag)" , "Small proportion" , "Small piece forming part of a whole" , "Fragment" .)