This is the 15039th most frequent Russian word.
поест
"Поест" means "will eat" or "will have a meal."
In this sentence, "поест" is used to indicate a future action, that the subject will finish eating.
Он поест и уйдёт.
He will eat and leave.
Here, "поест" is part of a suggestion or command, allowing someone to eat at their pace.
Дай ему немного времени: пусть поест.
Give him some time: let him eat.
In this sentence, "поест" is conditional, indicating an action that should occur within a specific timeframe.