Bad rum drunk around Eastern island group (7)
I believe the answer is:
bermuda
'island group' is the definition.
(territory made up 181 islands)
'bad rum drunk around eastern' is the wordplay.
'drunk' is an anagram indicator.
'around' indicates putting letters inside.
'eastern' becomes 'e'.
'bad'+'rum'='badrum'
'badrum' with letters rearranged gives 'brmuda'.
'brmuda' going around 'e' is 'BERMUDA'.
(Other definitions for bermuda that I've seen before include "British colony, capital Hamilton" , "Producer of rum" , "Island group in NW Atlantic" , "British self-governing overseas territory in the North Atlantic" , "NW Atlantic colony" .)