Greek character has time for mine (3)
I believe the answer is:
pit
'mine' is the definition.
(down the pit)
'greek character has time' is the wordplay.
'greek character' becomes 'pi' (letter from the Greek alphabet).
'has' means one lot of letters go next to another.
'time' becomes 't' (abbreviation).
'pi'+'t'='PIT'
'for' is the link.
(Other definitions for pit that I've seen before include "Tip into crater" , "where orchestra plays" , "Match (one's wits); mine" , "Mining hole" , "Large hole; fruit stone" .)