Island one wouldn't yield, if extremely resolute (4)
I believe the answer is:
inch
I believe this clue is a double definition.
'island' is the first definition.
(inch can mean a small island)
'one wouldn't yield if extremely resolute' is the second definition.
('don't give them an inch')
(Other definitions for inch that I've seen before include "Irish island" , "One of a 2 down in a foot" , "... or not so long < , Celtic island" , "Scottish island: unit of length" , "Move very slowly - a very short distance" .)