Bore shed tears about a Republican (7)
I believe the answer is:
carried
'bore' is the definition.
('carry' can be a synonym of 'bear')
'shed tears about a republican' is the wordplay.
'shed tears' becomes 'cried' (I've seen this in another clue).
'about' indicates putting letters inside.
'republican' becomes 'r' (abbreviation).
'a'+'r'='ar'
'cried' enclosing 'ar' is 'CARRIED'.
(Other definitions for carried that I've seen before include "Published" , "Bore" , "Conveyed, toted" , "passed by majority" , "maintained" .)