Some invited a US Republican over for influence (8)
I believe the answer is:
persuade
'for influence' is the definition.
(persuading is a kind of influencing)
'some invited a us republican over' is the wordplay.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'over' says the letters should be written backwards.
'edausrep' can be found hidden inside 'invited a us republican'.
'edausrep' backwards is 'PERSUADE'.
(Other definitions for persuade that I've seen before include "Convince or induce, maybe coax" , "Induce or convince to do something" , "'Coax, inveigle (8)'" , "Convince. cajole" , "Convince by argument" .)