Things started getting pretty confusing for the Halo continuity with Halo 5, as much of the campaign drew from events in the expanded Halo Universe. Blue Team, Fireteam Osiris, Guardians, much of the content in Halo 5 stemmed from the many novels and comic books that detailed the expanded Forerunner lore. However, it seems Halo Infinite is planning to recompile the main story back to the game. Part soft reboot, part sequel, Halo Infinite still features pretty significant villains from spin-off media. However, the events of Infinite are meant to be "a perfect starting point for new players" as well.
When Halo Infinite begins next year, the story will begin with a pretty sizable time jump after the events of Halo 5: Guardians. Two years in fact, as Halo Infinite is supposedly taking place in the canon year of 2560. There's still a series of events missing from the timeline between the UNSC discovering the Zeta Halo and Halo Infinite's beginning cutscene, which will likely be revealed during Halo Infinite's campaign. However, there is a significant amount of context from both Halo 5's ending, as well as the events of Halo Wars 2, that set up Halo Infinite's supposed plot. Here's everything in canon that's happened between Halo 5 and the beginning of Halo Infinite.
Where Halo 5: Guardians' Ending Leaves Things
After the Master Chief's failure to reason with the now untrustworthy Cortana, she is corrupted and merges with the Forerunner Domain network. Halo 5 concludes with a "cured" Cortana taking control over various UNSC artificial intelligences across the galaxy, all in a bid to enforce the "Mantle of Responsibility." The Mantle is a Forerunner philosophy that essentially enforces galactic peace through sheer Forerunner force, which happens to be why the Guardians were developed in the first place. Just as Cortana attempts to take over the UNSC Infinity, the UNSC-loyal AI Roland sends the Infinity into multiple random slipspace jumps to evade Cortana's guardians.
While the UNSC Infinity continues evasive maneuvers away from Cortana's pursuit, Fireteam Blue and Fireteam Osiris rendezvous with Dr. Halsey, Commander Palmer, and the Arbiter on the Sangheili (Elites) homeworld of Sanghelios. At this point, the majority of the UNSC's space fleet has been undermined by Cortana's annexation of the AIs throughout the galaxy. The UNSC Infinity was one of the very few uninfected by Guardians, and continues to flee after Halo 5's conclusion. Halo Infinite is set to begin in the year 2560, two years after the events of Halo 5, which means there's a huge gap in time unaccounted for. However, the events of Halo Wars 2 provide some clues on what to expect in Halo Infinite's story.
Important Context from Halo Wars 2
Halo Wars 2 serves as an interquel between Halo 5 and what will occur in Halo Infinite. The events of Halo Wars 2 are where Halo Infinite's antagonists are introduced to players for the first time. After spending around 28 years adrift in space, the UNSC Spirit of Fire's crew awakens in the orbit of the Ark, the Forerunner planetary array responsible with creating more Halo rings. Spirit of Fire's captain, Captain Cutter, orders an immediate investigation of a UNSC distress signal on the Ark's surface. After recovering an UNSC AI named Isabel, the recovery team is confronted by a subsect of Brute and former-Covenant mercenaries known as the Banished.
Those who watched the Halo Infinite gameplay were first introduced to a Banished lieutenant by the name of Escharum. Escharum is a War Chief under the command of Atriox, leader of the Banished. In Halo Wars 2, the Banished were first introduced as a rebellious group of ex-Covenant Brutes (and later Elites, Jackals, and Grunts) who were abused and betrayed by the Covenant's ruthless zealots. They broke ranks and headed for the Ark a few years prior to the Spirit of Fire arriving, and eventually clashed with the UNSC forces investigating the infamous Forerunner installation.
Adrift in space with no way to contact the rest of humanity (likely thanks to Cortana's meddling with AI as well), the Spirit of Fire crew intends to use the Ark to construct another Halo ring. The idea is to gather the crew on the new Halo and jump back to the Milky Way galaxy to UNSC-controlled space. However Anders, the human scientist who was rescued on the Ark, cannot halt the jump countdown after the new Halo is created. She, alone, promises the Spirit of Fire that she will call for UNSC assistance once she reaches friendly space. Anders' Halo jump is stopped prematurely by a Guardian, presumably but not confirmed as Cortana.
Then, that's supposedly where the events of Halo Infinite will begin. There's still a gap of time between when the UNSC discovers and investigates Zeta Halo, and when the Banished arrive there as well. Players will presumably learn how the UNSC lost as the Chief and the Pilot remember what happened at Installation 07.
Halo Infinite is planned to release in 2021.