Crossword Genius

Trump or head of state in the garden, perhaps (8)

Ross

I believe the answer is:

outdoors

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'garden perhaps' is the definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.

'trump or head of state' is the wordplay.
'trump' becomes 'outdo' ('outdo' can be a synonym of 'trump').
'head of' suggests taking the first letters.
The first letter of 'state' is 's'.
'outdo'+'or'+'s'='OUTDOORS'

'in the' is the link.

Can you help me to learn more?

(Other definitions for outdoors that I've seen before include "abroad" , "Alfresco" , "Al fresco" , "Not in a building" , "In the open air" .)

I've seen this clue in The Independent.
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