A Republican leading each district (4)
I believe the answer is:
area
'district' is the definition.
(I've seen this before)
'a republican leading each' is the wordplay.
'leading' suggests taking the first letters.
'each' becomes 'ea'.
The initial letter of 'republican' is 'r'.
'a'+'r'+'ea'='AREA'
(Other definitions for area that I've seen before include "Region, space" , "part of town" , "Expanse or neighbourhood" , "environs" , "field of study" .)