keep on a short leash(have/keep (someone) on a short/tight leash – to have a lot of control over someone's behaviour and allow them very little freedom to do what they want: He doesn't go out with the lads so much these days. Michelle keeps him on a tight leash Taras)
on the hook(- You know the drill, Bob. Be obedient and no one will know that you're on the hook.
- Ты знаешь правила игры, Боб. Подчиняйся, и тогда никто не узнает, что ты у меня на коротком поводке.Taras)