Determined a Duke should be borne by galloping steed (4,3)
I believe the answer is:
dead set
'determined' is the definition.
(I've seen this in another clue)
'a duke should be borne by galloping steed' is the wordplay.
'a duke' becomes 'd' (abbreviation).
'should be' becomes 'a' (I can't justify this - if you can you should give a lot more credence to this answer).
'borne by' indicates putting letters inside (to bear can mean to carry).
'galloping' indicates anagramming the letters (I've seen this in other clues).
'steed' is an anagram of 'edset'.
'a' going within 'edset' is 'eadset'.
'd'+'eadset'='DEAD-SET'
Can you help me to learn more?
(Other definitions for dead set that I've seen before include "Bent on - sedated (anag)" , "Absolutely - sedated (anag)" , "A determined attack - from extinct group?" , "Complete standstill; sedated (anag.)" , "Absolutely determined, bent on" .)