Despondency sadly besetting island in Middle East (7)
I believe the answer is:
malaise
'despondency' is the definition.
(thesaurus)
'sadly besetting island in middle east' is the wordplay.
'sadly' becomes 'malis' (I can't justify this - if you can you should believe this answer much more).
'besetting' means one lot of letters goes inside another.
'island' becomes 'Man' (the Isle of Man is an example).
'in middle' indicates the central letters.
'east' becomes 'e' (abbreviation).
The central letter of 'man' is 'a'.
'malis' going around 'a' is 'malais'.
'malais'+'e'='MALAISE'
Can you help me to learn more?
(Other definitions for malaise that I've seen before include "Out-of-sorts feeling" , "depression" , "Feeling of impending illness" , "Unease; lethargy" , "Uneasy feeling" .)