The old chaps meeting one Middle Eastern person (6)
I believe the answer is:
yemeni
'middle eastern person' is the definition.
(someone from Yemen)
'the old chaps meeting one' is the wordplay.
'the old' becomes 'ye' (resembles a historical spelling of 'the').
'chaps' becomes 'men' (chap means a man).
'meeting' is a charade indicator (letters next to each other).
'one' becomes 'i' (Roman numeral).
'ye'+'men'+'i'='YEMENI'
(Other definitions for yemeni that I've seen before include "From a country in the Arabian peninsula, capital Sana'a" , "Person from Sana'a, say" , "from an Arab country" , "Native of Sana'a, say" , "Arab national" .)