The Chainsawman manga came to an end; however, it also came with a pair of announcements. The first announcement was the television anime while the second announcement was that the manga would, indeed, be continuing in a second part. At the time, there were no details other than the fact that it was moving to the Shonen Jump+ app and website.
However, that changed as the story details for the second part have been revealed. Simply, the manga will be the “Gakkou-hen” arc in which Denji ends up going to school. The first part of the manga dealt with the “Koan” arc where Denji served in Public Safety.
VIZ Media is currently publishing the manga in North America and has released two volumes thus far. There are nine total volumes in the first part of the manga. The manga is also publishing in Shueisha’s MANGA Plus app in English.
As of right now, there is still no word as to when the second part will make its debut.