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

1.
在某人負責期間, 在某人任職期間
during the period when someone is responsible for something
:
•
The company's profits declined significantly on his watch.
公司利潤在他任職期間大幅下降。
•
I won't let anything bad happen to this project on my watch.
在我負責期間,我不會讓這個項目出任何問題。