One-time colony is overthrown when Greek character, almost late, provides cover (8)
I believe the answer is:
rhodesia
'one-time colony is overthrown' is the definition.
I can't tell whether this defines the answer.
'greek character almost late provides cover' is the wordplay.
'greek character' becomes 'rho' (letter of the Greek alphabet).
'almost' means to remove the last letter (almost the whole word is kept).
'late' becomes 'dec' (abbreviation for deceased).
'provides cover' becomes 'sia' (I can't justify this - if you can you should believe this answer much more).
'dec' with its final letter removed is 'de'.
'rho'+'de'+'sia'='RHODESIA'
'when' acts as a link.
Can you help me to learn more?
(Other definitions for rhodesia that I've seen before include "Former African country" , "Former British colony in central Africa" , "Previous name of Zimbabwe" , "place once overseen by Smith" , "What became Zimbabwe" .)