Spoilers for The Punisher Season 2 Episode 11 ahead. The Punisher's Frank Castle debuted on Daredevil, despite the fact that the character would never join The Defenders, and has stayed in his own bloodthirsty lane ever since. For that reason, it's difficult to trace his path in the Marvel universe. or even figure out when The Punisher Season 2 takes place? There aren't too many clues, but fans have some idea.
It appears that The Punisher takes place chronologically after Luke Cage Season 2 and specifically Daredevil Season 3, thanks to the appearance of two characters in the connected universe: small time crook and weapons dealer Turk Barrett, and investigative journalist Karen Page. A third returning character, Sargent Brett Mahoney, doesn't mention his past dealings with other Marvel vigilantes at all.
Midway through The Punisher Season 2, Turk appears and mentions to some criminal colleagues that he's been uptown, way uptown, for a while. That's likely referencing the Manhattan neighborhood of Harlem, where he was selling weapons for Luke Cage's antagonist Diamondback, though he did also appear in Iron Fist Season 2 suppling arms to Mary Walker.
Then, when Karen appears in Episode 11, things start to become a little more clear. Karen waltzes into Frank's heavily guarded hospital room by announcing herself as part of Nelson and Murdock's law firm, and therefore representing him. Before Daredevil Season 3, Matt Murdock was presumed dead, so that would have been a risky lie to tell. Ergo, I think it's safe to say that this is all taking place after Matt, Foggy, and Karen decide to get back into business together at the end of the third season.
As for how much actual time has passed between The Punisher Season 1 and Season 2? That's difficult to say. The first season ended with Frank Castle being broken out of jail, and Billy Russo being hospitalized. When the Netflix series picks back up, Castle is on the run and not keen to stay in one place for a very long time. Meanwhile, Russo has been in recovery for some months for his physical injuries and memory losses.
Season 1 premiered in November 2017 — is it possible that almost two years have passed since the events of Season 1? Marvel released an official timeline for the MCU, but that only includes the big screen Avengers films (and purports that Thanos' snap happened in 2017, but just ease your mind and presume that Endgame fixed that by the time we're checking in on the street-level Marvel heroes now). Still, that timeline alleges that the Marvel films take place chronologically and approximately around the year in which they were released.
So The Punisher Season 2 probably takes place just under a year after Season 1 ends. That's enough time for Frank to be crawling his way through Michigan and for Billy to have made months of progress.
Whether or not The Punisher will continue past this season is unknown, and unlikely considering that Daredevil, Luke Cage, and Iron Fist have all been canceled by Netflix. Without giving anything away, the ending of Season 2 leaves things open. At least Karen and Turk's appearances not only cement the season in a time and place, they prove that the MCU lives on, even if the shows are shutting down.