keep (someone) on a tight watch

Translations
держать (кого-то) под строгим наблюдением
The manager kept the new employee on a tight watch during the first month.
Менеджер держал нового сотрудника под строгим наблюдением в течение первого месяца.
Definitions
To closely monitor or supervise someone, often to ensure they do not engage in undesirable behavior or to keep them safe.