During the Clone Wars, Anakin is a Jedi Knight and has his own Padawan (Ahsoka).
Why didn't Obi-Wan take another Padawan apprentice?
Science Fiction & Fantasy Stack Exchange is a question and answer site for science fiction and fantasy enthusiasts. It only takes a minute to sign up.Sign up to join this community
Obi-Wan is on the Jedi Council, and thus no longer has an apprentice. We don't see any other member of the Council (Yoda, Windu, Ki-Adi-Mundi, etc.) with Padawans. They may teach Younglings in a class (as we see Yoda doing), but are no longer focused on ONE trainee. They are concerned with all Jedi, and the Republic as a whole, at that point.
Depa Billaba training Kanan Jarrus is a notable exception, but we only find that out after Star Wars Rebels was released. Since she didn't get much screen time in the movies, we can assume the restriction only applied to senior members of the Jedi Council.
The very short answer is that it was because it wasn't the will of the Jedi Council. At the start of the Clone Wars film, we learn that Kenobi did indeed discuss (with Yoda) the possibility of getting a new Padawan learner. Ahsoka Tano was sent, but in a surprise move Yoda assigned her to Anakin Skywalker rather than Kenobi.
The clear implication seems to be that Obi-Wan wasn't assigned a new Padawan because he was expected to keep an eye on the both of them.
"It'll be here," Kenobi said, exuding energy. As always, he seemed felt invigorated by a fight. Anakin wondered if he had those frenzied killing moments too. Kenobi hooked his lightsaber to his belt and jogged toward the plaza, where they'd set up a landing area. "Time for reinforcements, supplies, and perhaps my new Padawan."
Anakin's stomach sank a little. Dead weight. It distracted him from his brush with darkness not darkness, no and he seized it. A change of problem really was as good as a rest. "This isn't the time or the place to train a Padawan, Master. They're a liability." - Star Wars: The Clone Wars
On at least one occasion, Yoda threatened to transfer her guardianship to Obi-wan, something that wouldn't be a possibility if he was encumbered with his own learner
"Master Obi-Wan," he said, bowing. "Master Yoda." Yoda fixed him with a critical stare. "Trouble you have with your new Padawan, I hear." "I was explaining the situation to Master Yoda," Kenobi said. "If not ready for the responsibility of a Padawan you are, then perhaps to Obi-Wan she should go..." - Star Wars: The Clone Wars