Inspired by these questions Why did Palpatine order Anakin to kill Count Dooku when Anakin was not yet turned to the Dark Side? and If the Emperor and Vader agree to recruit Luke, doesn't that violate the Rule of Two?
In the Revenge of the Sith, Anakin incapacitates Tyranus. Then the Supreme Chancellor orders Anakin to kill Dooku. Anakin obeys the command of Palpatine, while he doesn't know that Palapatine is a Sith Lord at that time.
In Return of the Jedi same thing happened, but not exactly. Luke Skywalker incapacitates Darth Vader by cutting the hand of the Sith Lord.But the Emperor was very proud of it. Sidious even tries to convert Luke to the Dark Side. Unlike Anakin, Luke was able to resist it. He throws away his lightsaber and proclaiming himself a Jedi.
In these two situations that a Jedi defeats a Sith lord, why does Palpatine always want a new apprentice?