Money Greek character’s keeping at home (5)
I believe the answer is:
rhino
'money' is the definition.
(old-fashioned slang term for money)
'greek character's keeping at home' is the wordplay.
'greek character' becomes 'rho' (letter from the Greek alphabet).
'keeping' indicates putting letters inside (some letters kept inside).
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'rho' placed around 'in' is 'RHINO'.
(Other definitions for rhino that I've seen before include "When provoked, one may charge" , "Dosh (slang)" , "One charging" , "Large horned mammal" , "endangered creature" .)