The Republican accepts one belonging to them (5)
I believe the answer is:
their
'belonging to them' is the definition.
(I've seen this before)
'the republican accepts one' is the wordplay.
'republican' becomes 'R' (abbreviation in US politics).
'accepts' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'the'+'r'='ther'
'ther' going around 'i' is 'THEIR'.
(Other definitions for their that I've seen before include "Relating to them" , "Possessive pronoun" , "Some would say his (or her)" , "Those people's" , "Belonging to those people" .)