Televise cunning US chef's big vessel (8,7)
I believe the answer is:
aircraft carrier
'televise cunning us' is the definition.
I can't judge whether this definition defines the answer.
'chef's big vessel' is the wordplay.
'chef's big' becomes 'aircraft' (I can't justify this - if you can you should give a lot more credence to this answer).
'vessel' becomes 'carrier' (carrier is a kind of vessel).
'aircraft'+'carrier'='AIRCRAFT-CARRIER'
(Other definitions for aircraft carrier that I've seen before include "ship" , "warship" .)