People privy to information may have guts to cross Republican (8)
I believe the answer is:
insiders
'people privy to information' is the definition.
(people with inside information)
'guts to cross republican' is the wordplay.
'guts' becomes 'insides' (both can mean innards).
'to cross' means one lot of letters goes inside another.
'republican' becomes 'r' (abbreviation).
'insides' going around 'r' is 'INSIDERS'.
'may have' acts as a link.
(Other definitions for insiders that I've seen before include "Those privy to info" , "those with an advantage" , "Prisoners perhaps" , "Those privy to restricted information" , "They have an edge" .)