Republican base: some sent off to see a distant state (10)
I believe the answer is:
remoteness
'a distant state' is the definition.
(state or condition of being remote)
'republican base some sent off' is the wordplay.
'republican' becomes 'r' (abbreviation).
'base' becomes 'e' (Euler's number - base of natural logarithms).
'off' is an anagram indicator.
'some'+'sent'='somesent'
'somesent' with letters rearranged gives 'moteness'.
'r'+'e'+'moteness'='REMOTENESS'
'to see' acts as a link.
(Other definitions for remoteness that I've seen before include "Distant quality" , "Far-off quality" , "Aloof manner" .)