Hmmmm. For starters, I'd like to know how AU the Denmark of the tv show would be to current day Denmark. Because Denmark, along with much of the rest of the world, has drifted very much to the right. Especially on refugees. (See also here, and here.) Now of this, or something like this, has happened in the Borgen-verse, I can't see Birgitte still being a part of the government carrying out these policies, let alone Katrine as her spin doctor. (But then, my preference even for a best case scenario would be Katrine having returned to being a journalist as soon as the Free Democrats had made it as one of the coalition parties, because then her work - helping to create a new party and getting it to power - had been completed, and she is too good and passionate a journalist to give up on it.) Not unless the show is doing a bleak turn with their characters.
On the other hand, if a future season is set in a world where the fact that Birgitte returned to politics ten years ago and managed to create a new party giving people who like her had left her former party due to the later's rightward turn a voice, where she refused to become PM in a coalition with the right extremist party and became minister of foreign affairs in another Pm's covernment instead, where all of this ended up contributing to a situation where Denmark is currently pursueing different politics, then that's another matter, but then I'm not sure I won't feel too divorced from reality when watching it (call it the West Wing in the time of the Orange Menace problem). And I actually would like the characters debate about current day problems along with whatever is going on in their lives.
The third season had promoted Torben as the third most featured character (after Birgitte and Katrine), and I'd rather not get more of this, because I don't think he's interesting enough for that job. Kasper Juul was, though he also felt like his story was told by the end, so maybe a different character should get the No.3 attention spot. If Kasper is still around, I'd like for him and Katrine to continue as friendly exes rather than have yet another rerun of their on/off relationship. Of course, their son would be eleven or so years old, and given Kasper's whole backstory trauma, seeing how he copes with fatherhood now that the kid is old enough to talk back and ask questions could be interesting to explore; I'm just not sure whether it can fit in a mainly political drama.
Birgitte's kids are both adults by now, and that probably means the scriptwriters don't face the temptation for another go at "am I a bad mother for devoting myself to politics?" I'm probably the sole Borgen fan who isn't into Philipp, so I'm not rooting for her to get back together with him, though I'll cope if she does. Mainly I hope that whether she's an opposition politician or whether she decided to figure out other ways to shape the world, she got to wherever she is now by her own choices, which is always more interesting, be they good or bad ones. Honestly, I don't know how viable it is for a tv setting of a Danish show, but my secret dream job for Birgitte at this point of her life would be EU Commissioner - what Ursula von der Leyen is doing right now. Birgitte having to switch between diplomacy and butting heads with various heads of state and parliamentarians from various nations would be very rewarding dramatically, imo.
For Hanne, I hope she's managed to stay sober and in journalism, though given how the trends Borgen already showcased in the media development continued, I fear her being out of a job is all too likely. And if Borgen goes at all near rl heads of state, I predict a round of collective journalistic despair about how it doesn't even seem to matter anymore if you break a story about someone's evil deeds, they just brazen it out, deny it, say "fake news" and do something even worse the next time.
Lastly, I think it's inevitable we'll see some new characters, because even the younger ones like Katrine are now veterans of their profession, and because it could be interesting drama if our heroes face
Incidentally, there are still free days, if you want me to talk about another topic...
The Other Days