Georgia's capital (7)
'georgia's capital' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for tbilisi that I've seen before include "Georgian capital" , "Capital city of Georgia" , "Georgian city" , "Georgian place" .)
(Other definitions for augusta that I've seen before include "Scene of annual US" , "Masters course" , "US city" , "American city" , "Lady Bracknell" .)