Capital in Washington, I note, a US city (7)
I believe the answer is:
wichita
'us city' is the definition.
(I've seen this before)
'capital in washington i note a' is the wordplay.
'capital in' indicates taking the first letters.
'note' becomes 'chit' (I've seen this before**).
The first letter of 'washington' is 'w'.
'w'+'i'+'chit'+'a'='WICHITA'
(Other definitions for wichita that I've seen before include "US city" , "city in America" , "place in Kansas" , "Kansas city" .)