Recover month, going round a state (7)
I believe the answer is:
vermont
'a state' is the definition.
(I know that Vermont is a American state)
'recover month going round' is the wordplay.
'going round' indicates a hidden word.
'VERMONT' is hidden within 'recover month'.
(Other definitions for vermont that I've seen before include "New England state, capital Montpelier" , "US state, named for the Green Mountains" , "The Green Mountain state" .)