Put your towel, if not your shirt, on it (5)

I believe the answer is:
horse
'put' is the definition.
The answer and definition can be both related to consumption as well as being verbs in their base form.
Perhaps they are linked in a way I don't understand?
'your towel if not your shirt on it' is the wordplay.
I cannot really see how this works, but
'not' could be 'o' (I've seen this in other clues) and 'o' is found in the answer.
'it' could be 'e' ('e' can mean 'electronic' which is similar to 'IT') and 'e' is located in the answer.
The remaining letters 'hrs' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for horse that I've seen before include "It may get people stoned" , "punch, perhaps" , "Roan" , "farm animal" , "Nag, hack" .)