Descending Stories: Showa Genroku Rakugo Shinju

Showa Genroku Rakugo Shinjuu is a manga by Haruko Kumota. It was adapted into two OVAs then an anime and was part of the winter 2016 anime season.

Plot
As soon as an ex-con gets out of prison, he goes to Yakumo Yurakutei the rakugo master. Yakumo performed a play called "Shinigami" in the past, motivating the former criminal to take up rakugo himself. After Yakumo takes him in without much reluctance, he has to live up to his master's standards while coping with his past and Yakumo's ward Konatsu.

Official
http://rakugo-shinju-anime.jp/