Join snub about independent state (11)
I believe the answer is:
connecticut
'state' is the definition.
(Connecticut is an example)
'join snub about independent' is the wordplay.
'join' becomes 'connect' ('connect' can be a synonym of 'join'**).
'snub' becomes 'cut' ('cut' can be a synonym of 'snub').
'about' is a charade indicator (letters next to each other).
'independent' becomes 'i'.
'cut' put after 'i' is 'icut'.
'connect'+'icut'='CONNECTICUT'
(Other definitions for connecticut that I've seen before include "One of original thirteen US states" , "State of NE USA" , "America" , "state of the union" , "Yale U. is in this US state" .)