Duke is captivated by foxtrot and tango (4)
I believe the answer is:
fist
'duke' is the definition.
(put up your dukes)
'is captivated by foxtrot and tango' is the wordplay.
'captivated by' indicates putting letters inside.
'foxtrot' becomes 'f' (phonetic alphabet: alpha, bravo, charlie etc.).
'and' says to put letters next to each other.
'tango' becomes 'T' (phonetic alphabet: alpha, bravo, charlie etc.).
'f'+'t'='ft'
'is' going into 'ft' is 'FIST'.
(Other definitions for fist that I've seen before include "Balled hand" , "duke" , "One may deck in a ring" , "Hand with the fingers clenched in the palm" , "Bunch of fives" .)