Gets the better of openly gay deer? (7)

I believe the answer is:

outdoes

I'm a little stuck... Click here to teach me more about this clue!

'gets the better of' is the definition.
The definition and answer can be both related to competing as well as being verbs in their -s form.
Perhaps you can see a link between them that I can't see?

'openly gay deer?' is the wordplay.
'openly gay' becomes 'out' (I've seen this before).
'deer?' becomes 'does' (I've seen this in other clues).
'out'+'does'='OUTDOES'

Can you help me to learn more?

I've seen this clue in The Independent.

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