Hesitate to be awfully rude about a military leader (5)
I believe the answer is:
demur
'hesitate' is the definition.
(thesaurus)
'awfully rude about a military leader' is the wordplay.
'awfully' is an anagram indicator.
'about' means one lot of letters goes inside another.
'leader' indicates taking the first letters.
The first letter of 'military' is 'm'.
'rude' with letters rearranged gives 'deur'.
'deur' going around 'm' is 'DEMUR'.
'to be' is the link.
(Other definitions for demur that I've seen before include "Waver" , "Balk" , "Hesitation" , "Raise objections" , "Take exception (to)" .)