Tom’s riding a horse or some other animal? (9)

'some other animal?' is the definition.
'catamount' can be an answer for 'animal?' (thesaurus). I'm unsure of the 'some other' bit.

'tom's riding a horse' is the wordplay.
'tom' becomes 'cat' (I have seen 'A tom ' mean 'cat' so perhaps 'tom' could also mean 'cat').
'riding' says to put letters next to each other (in a down clue, some letters go on top of others).
'horse' becomes 'mount' (mount is a kind of horse).
'cat'+'a'+'mount'='CATAMOUNT'

'or' is the link.

Can you help me to learn more?