On someone's watch phrase informal
During the time when one is in a position of power and in charge of supervising someone or something
The accident happened to the kid on her watch, so she was harshly criticized.
He decided to quit his position as a manager due to recent mistakes on his watch.
To oversee someone or something carefully
If you say that you keep (someone or something) in check, you mean that you keep them under control.
To be thankful or grateful for one's good luck usually while avoiding a bad situation
You should count your lucky stars as you managed to avoid that violent car accident.