Idiom
keep close watch on somethingkeep (a) close watch on (someone/something)
to guard or follow carefully someone or something.With an international team keeping close watch on polling stations, voters chose from an array of 12 candidates.Republicans are warning the president to keep a close watch on spending.
Usage notes: sometimes used in the form keep a watch on:
He wants to keep a watch on who comes and goes from the office.
Related vocabulary: keep an eye out for someone/something