Entrance by duke - that is a determined effort to succeed (2,2,3)
I believe the answer is:
do or die
'a determined effort to succeed' is the definition.
I don't know anything about this answer so I cannot judge whether this works.
'entrance by duke that is' is the wordplay.
I cannot really understand how this works, but
'entrance' could be 'door' (door is a kind of entrance) and 'door' is located in the answer.
'duke' could be 'd' (abbreviation) and 'd' is found within the answer.
'that is' could be 'ie' (short for Latin 'id est', 'that is') and 'ie' is located in the answer.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for do or die that I've seen before include "Make a desperate effort whatever the consequences" , "Stark choice" , "doggedly determined" , "with dogged determination" , "Rash" .)