Hound beginning to howl, heading off bear (5)
I believe the answer is:
harry
'hound' is the definition.
(both can mean to harass)
'beginning to howl heading off bear' is the wordplay.
'beginning to' suggests taking the first letters.
'heading off' means to remove the first letter.
'bear' becomes 'carry' (bear can mean to carry).
The first letter of 'howl' is 'h'.
'carry' with its initial letter removed is 'arry'.
'h'+'arry'='HARRY'
(Other definitions for harry that I've seen before include "See 20" , "Hector" , "Harass; man's name" , "Make predatory raids" , "Male" .)