Most important US state dropping back (4)
I believe the answer is:
main
'most important' is the definition.
(I've seen this before)
'us state dropping back' is the wordplay.
'us state' becomes 'maine' (I've seen this before).
'dropping back' means to remove the last letter.
'maine' with its final letter taken away is 'MAIN'.
(Other definitions for main that I've seen before include "(The mighty) sea" , "Source of water" , "Chief, primary" , "associated with the Spanish?" , "Chief in importance" .)