Crossword Genius

Excited meeting president where babies go to eat (4,5)

Ross

I believe the answer is:

high chair

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

'where babies go to eat' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how they can define each other.

'excited meeting president' is the wordplay.
I cannot quite see how this works, but
'excited' could be 'high' (I've seen this in other clues) and 'high' is located in the answer.
'president' could be 'chair' (synonyms) and 'chair' is present in the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for high chair that I've seen before include "It raises the issue" , "Seat for baby at table" , "one supporting young scoffers?" , "Position of senior academic" , "senior professional post" .)

I've seen this clue in The Guardian.
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