Struck about Republican being insulted online (7)
I believe the answer is:
trolled
'insulted online' is the definition.
'struck about republican' is the wordplay.
'struck' becomes 'tolled'.
'about' is an insertion indicator.
'republican' becomes 'r' (abbreviation).
'tolled' enclosing 'r' is 'TROLLED'.
'being' is the link.
(Other definitions for trolled that I've seen before include "posted offensive comment" , "Made provocative comments" .)