US rock star trashed rooms across Rhode Island -- indefinite number (8)
I believe the answer is:
morrison
'us rock star' is the definition.
(Jim Morrison of The Doors)
'trashed rooms across rhode island indefinite number' is the wordplay.
'trashed' indicates anagramming the letters (I've seen this in other clues).
'across' indicates putting letters inside.
'rhode island' becomes 'ri' (US postal abbreviation).
'indefinite number' becomes 'n' (mathematical symbol).
'rooms' is an anagram of 'morso'.
'morso' enclosing 'ri' is 'morriso'.
'morriso'+'n'='MORRISON'
(Other definitions for morrison that I've seen before include "'Van, Jim and Toni (8)'" , "wartime shelter" .)