Check old rule out (4)
I believe the answer is:
veto
'rule out' is the definition.
(to veto something is to block it or rule it out)
'check old' is the wordplay.
'check' becomes 'vet' (to vet someone is to check their background).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'vet'+'o'='VETO'
(Other definitions for veto that I've seen before include "Blocking vote" , "Throw out" , "Power to reject legislation" , "Right to ban" , "Formally forbid" .)