Cap soldiers had at Kitchener’s offensive, initially? (5)
I believe the answer is:
shako
'cap' is the definition.
'soldiers had at kitchener's offensive initially?' is the wordplay.
'initially?' indicates taking the first letters (I've seen 'initially' mean this).
The initial letters of 'soldiers had at kitchener offensive' is 'SHAKO'.
(Other definitions for shako that I've seen before include "Old mil. headdress" , "Capital cover" , "One covering for military head" , "Tall military cap" , "military headdress" .)