As the industry reels from the announcement of Xbox's merger with Activision Blizzard, details of the new pairing have continued to trickle out from both sides. Of course, gamers' main concerns are focused on what Microsoft will allow to still come to PlayStation and Switch consoles after the merger is complete (if any come at all) and more importantly, what established games will be kept on previous platforms. Activision Blizzard has confirmed that existing games will be kept on their respective platforms, much like how Microsoft handled Bethesda titles.
Coming from an employee Q&A filed with the Securities and Exchange Commission, Activision Blizzard has stated that the company will indeed honor any and all pre-existing deals and established titles on other platforms. The company says that similar to Microsoft's acquisition of Minecraft, Activision Blizzard has no intention of removing any content from where it rests today. What this means is that all previous titles, including ongoing titles such as Call of Duty: Warzone, will continue to be sold and updated on PlayStation consoles.
With all that being said, whether new titles will be arriving on PlayStation consoles is a whole other story. While it is possible that Microsoft will want to keep Call of Duty appearing on other platforms considering the gigantic amount of money the series makes, a company doesn't pay almost $70 billion just to allow another company to make money off one of its franchises.
Activision Blizzard has said that it won't prematurely end any contracts it has with Sony as Sony has recently said that it expects Activision Blizzard and Microsoft to uphold any existing contracts currently in place. It is not exactly clear what these contracts entail or for how long Microsoft will have to honor them for. Again, similar to the Bethesda acquisition and the releases of Deathloop and the upcoming Ghostwire:Tokyo, it is likely some games or content will arrive on Sony's platform first and then come to Xbox up to a year after release.
However, gamers attached to Call of Duty should start to come to terms with the fact that like Starfield and The Elder Scrolls 6, future Call of Duty titles (besides 2022's iteration) will possibly be exclusive to Xbox and will appear day-one on Xbox Game Pass. It still is a future that is hard to believe, but it's possible the beginning of the end of Activision Blizzard games on PlayStation's consoles has begun.
Source: IGN