A million involved in fast must be keen (6)
I believe the answer is:
lament
'keen' is the definition.
(keen can mean to wail with grief)
'a million involved in fast' is the wordplay.
'million' becomes 'm' (abbreviation).
'involved in' is an insertion indicator.
'fast' becomes 'lent' (Lent is a period of fasting in Christianity).
'a'+'m'='am'
'am' put inside 'lent' is 'LAMENT'.
'must be' is the link.
(Other definitions for lament that I've seen before include "Complain" , "Wail" , "Mourning song or poem" , "Mourn (a person's death)" , "Bemoan, bewail" .)