African or Irish singer in outskirts of Kingston (6)
I believe the answer is:
kenyan
'african' is the definition.
(Kenyan is an example)
'irish singer in outskirts of kingston' is the wordplay.
'irish singer' becomes 'enya' (I've seen this in another clue).
'in' is an insertion indicator.
'outskirts of' means to remove the middle letters (only letters on the outskirts).
'kingston' with its centre removed is 'kn'.
'enya' placed into 'kn' is 'KENYAN'.
'or' acts as a link.
(Other definitions for kenyan that I've seen before include "person in Africa" , "East African" , "One from Nairobi" , "Nationality of native of Nairobi" , "Commonwealth citizen" .)