Crossword Genius

Hoover, say, has got stuck in like US president (5)

Ross

I believe the answer is:

adams

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

'us president' is the definition.
(I've seen this before)

'hoover say has got stuck in' is the wordplay.
I cannot quite understand how this works, but
'hoover' could be 'dam' (I've seen this in another clue) and 'dam' is located in the answer.
'say' could be 'as' (I've seen this in other clues) and 'as' is found within the remaining letters.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

'like' acts as a link.

Can you help me to learn more?

(Other definitions for adams that I've seen before include "Father and son were American presidents" , "revolutionary leader" , "Father and son US presidents" , "Sort of apple" , "Former US president" .)

I've seen this clue in The Times.
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