The whole continuity shebang explained

While it is Season 3, Book of Circus functions as a quasi reboot/alternate sequel to Black Butler Season 1, ignoring the events of Season 2 and the earlier OVAs.

Basically, everything from Episode 6 of BBS1 (the end of the Ripper arc) is ignored, with BOC taking place sometime after the funeral of Madam Red and meeting Grell, but before the Hound arc (so no Pluto) and before the whole Angel business (the cult that murdered the Phantomhives here is slightly altered, and Ash is replaced by different advisors to a much older Queen Victoria). Some recycling of footage and images from the first six episodes further support this, and even though Soma and Agni make an appearance, the flashback is edited to remove any mention of Ash or the altered ´Victoria´, so a different version of the basic encounter can be inferred.

Also, the first episode has a brief recap of the origin of the pact, but more in a real world perspective rather than the metaphysical, like the feather realm from S1, so nothing is out and out contradicted here. If you hated S2, you can write it off completely and go back to the early section of S1 and continue the original story, or, if you also didn´t like S1, BOC offers the needed intro to establish everything and get things rolling as its own story.

Either way, nice move on the part of the production team: the manga fans get a series closer to their material, and the anime fans don´t feel like they wasted their time watching the original series. Props.