One of the more surprising efforts made by Bungie during its time with the Halo franchise was Halo 3: ODST, a spin-off shooter not lead by Master Chief. Featuring the iconic special forces of the Halo universe in starring roles, Halo 3: ODST was the first (and last) first-person shooter where players didn't play as a Spartan. Even Halo: Reach, despite not featuring the Master Chief at all, was far different in scope because at the end of the day, players were still Spartans. Halo 3: ODST emphasized a specific vulnerability and confidence of the franchise in many ways, arguably moreso than Reach, that a Halo Infinite spin-off could similarly recapture.
Even as development marches along for Halo Infinite's fall 2021 release, an ODST style spin-off would be a welcome surprise, assuming Infinite succeeds. Understandably, 343 Industries kind of has to play it safe with Halo Infinite, regardless of how many people still enjoyed Halo 5. However, assuming Infinite does well to usher in the new generation of Halo games, following up with a spin-off in the same vein as Halo 3: ODST would be a perfect intermediary release before the next major Halo game. There are still various facets of Halo's world outside of the Master Chief's perspective that 343 should explore, without interrupting Halo Infinite's long-term momentum.
What's special about Halo 3: ODST is that it grew exponentially from a humble expansion of the base Halo 3 experience into a full-on standalone release. Bungie had the confidence to take players away from the Master Chief, if briefly, to tell a story usually relegated to the many Halo novels and other forms of media. Since 343 Industries has taken the mantle of responsibility for the Halo franchise, it's spread about equal halves of its time playing it safe and experimenting with storytelling. Halo 4 played out relatively neutral through a largely exterior and standalone story for the Master Chief, while Halo 5: Guardians took many creative liberties in the follow-up.
However, many fans had expressed discontent with Halo 5. Not only did the game (and, to some extent, its marketing) set expectations for what would be a very different Halo game, but the campaign in particular was a major gripe for many. On the flip side, Halo Wars 2 was an ambitious effort by 343 Industries to tell an original Halo story, and it was largely received positively. Even if the game didn't have a particularly climactic ending, it did potentially set up for a tie-in to Halo Infinite with its cliffhanger ending. 343 Industries certainly has the chops to tell an original Halo story, it just hasn't quite found its balance with the series post-Bungie.
Assuming Halo Infinite receives positive critical/commercial reception, that could certainly open up the possibility of an in-universe Halo spin-off. Whether that's likely or not is a whole different question, even though 343 Industries' Bonnie Ross has encouraged the idea of more Halo spin-offs in the future. However, assuming 343 Industries wants to take the ambitious route of storytelling between mainline Halo entries, there's plenty of source material and events throughout Halo canon worth exploring. Similar to Halo 3: ODST, there's a couple key points in Halo's past ripe for storytelling opportunities.
The most immediate focus would be the gap in time between Halo 5: Guardians and the supposed year Halo Infinite is meant to take place. Not counting the events of Halo Wars 2, there's about two years of in-universe time between the two mainline Halo games. Obviously, based on what Halo Infinite has already teased at length, humanity suffered a huge loss at the hands of the Banished. Regardless of whether or not Master Chief was there or not, it'd be interesting if those specific events were the subject of a spin-off story. Halo Infinite will undoubtedly touch on what happened, though it necessarily won't have the same specificity as a standalone game.