eager beaver
eager beaver {n. phr.}, {slang}
A person who is always eager to work or do anything extra, perhaps to win the favor of his leader or boss.
Jack likes his teacher and works hard for her, but his classmates call him an eager beaver.
The man who was promoted to be manager was an eager beaver who got to work early and left late and was always offering to do extra work.
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Source: A Dictionary of American Idioms
