Do not admit from Delaware and New York (4)
I believe the answer is:
deny
'do not admit' is the definition.
(I've seen this before)
'delaware and new york' is the wordplay.
'delaware' becomes 'de' (standard two letter abbrev).
'and' means one lot of letters go next to another.
'new york' becomes 'ny'.
'de'+'ny'='DENY'
'from' acts as a link.
(Other definitions for deny that I've seen before include "Refuse to accept" , "Refuse to admit (something)" , "Declare not to be true" , "Declare untrue" , "Refuse to admit the truth" .)