be on the watch (for someone or something)

To be closely monitoring for someone or something, usually in an attempt to avoid danger. You need to be on the watch for suspicious people when you're out in the city this late at night. Be on the watch for grammar errors—this writer is notorious for run-on sentences. Customers need to be on the watch for fraudulent emails and phone calls asking for bank details and account passwords.

be on the ˈwatch (for somebody/something)

be looking carefully for somebody/something that you expect to see, especially in order to avoid possible danger: The police warned tourists to be on the watch for car thieves.