Boredom of Northern Greek character in East Indies (5)
I believe the answer is:
ennui
'boredom' is the definition.
('ennui' can be a synonym of 'boredom')
'northern greek character in east indies' is the wordplay.
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'greek character' becomes 'nu' (letter from the Greek alphabet).
'in' indicates putting letters inside.
'east indies' becomes 'ei' (abbreviation).
'n'+'nu'='nnu'
'nnu' put within 'ei' is 'ENNUI'.
'of' is the link.
(Other definitions for ennui that I've seen before include "boring" , "Sense of tedium" , "Mental weariness" , "World-weariness" , "having nothing to do" .)