After a half-day, could say 'Djiboutian' (7)
I believe the answer is:
african
'djiboutian' is the definition.
The definition and answer can be both people as well as being singular nouns.
Maybe there's an association between them I don't understand?
'after a half-day could' is the wordplay.
'after' says to put letters next to each other.
'a' becomes 'an'.
'half' suggests halving the letters.
'day' becomes 'fri'.
'could' becomes 'can' (I can't explain this - if you can you should give a lot more credence to this answer).
'an' with half the letters taken is 'a'.
'a' next to 'fri' is 'afri'.
'afri'+'can'='AFRICAN'
'say' acts as a link.
Can you help me to learn more?
(Other definitions for african that I've seen before include "Person from, eg, Congo" , "from Liberia?" , "One from south of the Mediterranean" , "Bogart's Queen" , "Kenyan, perhaps" .)