Queen of island beset by mounting fury (6)
I believe the answer is:
regina
'queen' is the definition.
(I've seen this before)
'island beset by mounting fury' is the wordplay.
'island' becomes 'i'.
'beset by' indicates putting letters inside ('beset' could historically mean 'cover').
'mounting' is a reversal indicator (going up in a down clue).
'fury' becomes 'anger' (I've seen this before).
'anger' written backwards gives 'regna'.
'i' placed inside 'regna' is 'REGINA'.
'of' acts as a link.
(Other definitions for regina that I've seen before include "Title of reigning Queen" , "monarch" , "in Canada" , "Victoria?" , "our head of state" .)