Left-wing material: it starts to parody Reagan (amongst America’s foremost Republicans) (8)
I believe the answer is:
agitprop
'left-wing material' is the definition.
(term for communist propaganda)
'it starts to parody reagan amongst america's foremost republicans' is the wordplay.
'starts to' suggests taking the first letters.
'amongst' is an insertion indicator (I've seen this in other clues).
'foremost' indicates taking the first letters.
'republicans' becomes 'gop' (Grand Old Party, nickname for the Republican Party).
The initial letters of 'parody reagan' is 'pr'.
The first letter of 'americas' is 'a'.
'it'+'pr'='itpr'
'a'+'gop'='agop'
'itpr' going within 'agop' is 'AGITPROP'.
(Other definitions for agitprop that I've seen before include "Revolutionary stirring" , "subversive literature" , "political hype" , "Culturally delivered political propaganda -- a top grip (anag)" , "Politically loaded material" .)