Duke cutting a deck to deal with (7)
I believe the answer is:
address
'deal with' is the definition.
(synonyms)
'duke cutting a deck' is the wordplay.
'duke' becomes 'd' (abbreviation).
'cutting' indicates putting letters inside (some letters cut their way into a word).
'deck' becomes 'dress' (I've seen this before).
'a'+'dress'='adress'
'd' inserted within 'adress' is 'ADDRESS'.
'to' acts as a link.
(Other definitions for address that I've seen before include "Speech - written on an envelope?" , "One's postal residence." , "Speak formally to an audience" , "Speak to the residence" , "Direct words at" .)