Dog beginning to burrow great hole on course (6)
I believe the answer is:
beagle
'dog' is the definition.
(I know that beagle is a type of dog)
'beginning to burrow great hole on course' is the wordplay.
'beginning to' says to take the initial letters.
'great' becomes 'G' (abbreviation in place names).
'hole' becomes 'eal' (I can't explain this - if you can you should believe this answer much more).
'on' indicates putting letters inside (as in clothing 'on' a person).
'course' becomes 'e'.
The initial letter of 'burrow' is 'b'.
'g' placed inside 'eal' is 'eagl'.
'b'+'eagl'+'e'='BEAGLE'
(Other definitions for beagle that I've seen before include "Small hunting dog" , "Darwin voyaged in this ship" , "Small short-legged hound" , "Type of hound" , "Small, sturdy breed of hound" .)