Song of Republican over in California (5)
I believe the answer is:
carol
'song' is the definition.
(carol is a kind of song)
'republican over in california' is the wordplay.
'republican' becomes 'r' (abbreviation).
'over' becomes 'o' (cricket abbreviation).
'in' indicates putting letters inside.
'california' becomes 'cal' (short for California).
'r'+'o'='ro'
'ro' put into 'cal' is 'CAROL'.
'of' acts as a link.
(Other definitions for carol that I've seen before include "Girl's name; sing" , "Joyful religious song" , "Joyful song - woman's name" , "Religious song - girl's name" , "and 27: Waits" .)