Island that's really dreary to the west, graduate inhabiting it (8)
I believe the answer is:
barbados
'island' is the definition.
(island nation)
'really dreary to the west graduate inhabiting it' is the wordplay.
I cannot quite see how this works, but
'graduate' could be 'ba' (someone with a Bachelor of Arts degree) and 'ba' is found within the answer.
This explanation may well be incorrect...
'that's' is the link.
Can you help me to learn more?
(Other definitions for barbados that I've seen before include "Absorb ad about the West Indian island" , "Popular resort in the West Indies" , "Island in West Indies, capital Bridgetown" , "holiday island" , "Island place" .)