This is a very difficult question to answer. The first season of "Bodyguard" was released in August and September of 2018, and British shows are notoriously slow at producing new seasons, so fans knew it would be a while before new episodes came out. As of right now, the series isn't officially renewed or cancelled, but that doesn't mean much, as Madden, Mercurio, and others involved with "Bodyguard" have been commenting on a second season ever since the first ended, and it seems practically guaranteed. The question is just when.
In an interview with Deadline back in 2018, shortly after BBC's "Bodyguard" hit Netflix, Madden seemed quite sure that Season 2 would happen, saying, "I'm going to meet Jed in a couple of weeks, to have a chat and see what's in his brilliant brain." In mid-2019, Mercurio confirmed at the Banff World Music Festival that he was in talks with BBC, but that Season 2 was not officially greenlit (via The Hollywood Reporter). In late 2019, actor Nicholas Gleaves, who played Roger Penhaligon in "Bodyguard" Season 1, told RadioTimes that he spoke with a producer who "absolutely guaranteed" a second season, but until it's official, it's still up in the air.
Now in 2021, Madden has his roles in "From Now" and "Eternals" out of the way, leaving his schedule relatively open to return to "Bodyguard." Looking at the timeline, the earliest new episodes could come out is likely late next year or early 2023, unless BBC gets going on production really quickly.