Soldier supporting head of cat or dog (5)
I believe the answer is:
corgi
'dog' is the definition.
(I know that corgi is a type of dog)
'soldier supporting head of cat or' is the wordplay.
'soldier' becomes 'GI' (GI can mean a US soldier).
'supporting' says to put letters next to each other (in a down clue, some letters go below others).
'head of' suggests taking the first letters.
The first letter of 'cat' is 'c'.
'c'+'or'='cor'
'gi' put after 'cor' is 'CORGI'.
(Other definitions for corgi that I've seen before include "Dog of Welsh breed, royal favourite" , "Pre-2018 royal dog" , "The Queen's favourite?" , "Welsh breed of short-legged dog" , "Cardigan or Pembroke dog" .)