Dog right in between officer and private (5)
I believe the answer is:
corgi
'dog' is the definition.
(I know that corgi is a type of dog)
'right in between officer and private' is the wordplay.
'right' becomes 'r' (common abbreviation).
'in between' indicates putting letters inside.
'officer' becomes 'co' (Commanding Officer abbreviation).
'and' says to put letters next to each other.
'private' becomes 'GI' (GI can informally mean a US soldier).
'co'+'gi'='cogi'
'r' placed within 'cogi' is 'CORGI'.
(Other definitions for corgi that I've seen before include "Cardigan or Pembroke dog" , "Dog at Buckingham Palace" , "Welsh 11" , "The Queen's favourite?" , "Dog of Welsh breed, royal favourite" .)