on someone's watch
US /ɑn ˈsʌm.wʌnz wɑtʃ/
UK /ɑn ˈsʌm.wʌnz wɑtʃ/

1.
在某人负责期间, 在某人任职期间
during the period when someone is responsible for something
:
•
The company's profits declined significantly on his watch.
公司利润在他任职期间大幅下降。
•
I won't let anything bad happen to this project on my watch.
在我负责期间,我不会让这个项目出任何问题。