Dog commanding officer to start running with soldier (5)
I believe the answer is:
corgi
'dog' is the definition.
(corgi is a kind of dog)
'commanding officer to start running with soldier' is the wordplay.
'commanding officer' becomes 'co'.
'to start' suggests taking the first letters.
'with' says to put letters next to each other.
'soldier' becomes 'GI' (term for US soldier).
The initial letter of 'running' is 'r'.
'co'+'r'+'gi'='CORGI'
(Other definitions for corgi that I've seen before include "Small Welsh dog with fox-like head" , "Pre-2018 royal dog" , "Queen's dog?" , "Cardigan or Pembroke dog" , "The Queen's favourite?" .)