Knight's half of republic's capital (3)
I believe the answer is:
dub
'knight's' is the definition.
(to dub can mean to knight someone)
'half of republic's capital' is the wordplay.
'half of' means to take half the letters.
'republic's capital' becomes 'Dublin' (capital of the Republic of Ireland).
'dublin' halved is 'DUB'.
(Other definitions for dub that I've seen before include "Raise to knighthood" , "Copy to tape or disc" , "Reggae" , "type of music" , "Confer a title on" .)