Patrolled, with due deference to duke (5)
I believe the answer is:
paced
'patrolled' is the definition.
'with due deference to duke' is the wordplay.
'with due deference to' becomes 'pace' (Latin term meaning 'with due respect to').
'duke' becomes 'd'.
'pace'+'d'='PACED'
(Other definitions for paced that I've seen before include "set the tempo" , "Took steps" , "Moved steadily" , "Walked about in a preoccupied or frustrated way" , "Measured (a distance) by walking" .)