keep tabs on

See tab (“tablet or slate used for keeping a record of accounts”).

• "If you are careful to keep tabs on your finances, you should be able to stay within a budget."
• "The police kept close tabs on him during the holidays."
• "He might have spent the hours camped under the trees of the more remote meadow, whence in the brilliant moonlight he could keep tabs on the trails."
• "I'll catch him—I'll trip him up—I'll keep tabs on his arguments."
• "Syria's much feared state-security apparatus keeps close tabs on everyone entering and leaving the embassy."
• "Nadal, absent from the draw for the first time nearly two decades, said he won’t watch it all from afar, but he will be keeping tabs."