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

1.
〜の監視下で, 〜の責任において
during the period when someone is responsible for something
:
•
The company's profits declined significantly on his watch.
会社の利益は彼の監視下で大幅に減少した。
•
I won't let anything bad happen to this project on my watch.
私の監視下で、このプロジェクトに何か悪いことが起こるのを許さない。