Live temporarily with American in hovel (4)

I believe the answer is:

stay

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'live temporarily' is the definition.
'stay' can be an answer for 'live' (thesaurus). I am not certain of the 'temporarily' bit.

'american in hovel' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'in' indicates putting letters inside.
'hovel' becomes 'sty' (I've seen this in another clue).
'a' inserted into 'sty' is 'STAY'.

'with' acts as a link.

Can you help me to learn more?

(Other definitions for stay that I've seen before include "Support, delay" , "guy giving > support" , "guy to > put off" , "Stanchion" , "Remain; brace" .)

I've seen this clue in The Times.

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