1) Include an episode - or a whole story arc - somewhere in Season 1 where it turns out the Maquis - or some of them - are not as happy to be friends with Starfleet as we saw them on Parallax. Get them in a conflict with Starfleet WITHOUT giving Seska a major role in this so that she can go on plotting with the Kazon the way she actually did on the show.
2) Have more stories about Seska and the Kazon planning their attack on Voyager. Have more secret communications between them, etc. and show that Seska and Michael Jonas had already been planning to do something major against Voyager before Jonas's story arc happens in Season 2. (Whatever they were trying to do before the events in Season 2 was foiled for some good reason.)
3) Susperia's story. Get the female Caretaker involved with Voyager a lot more and potentially make Endgame a story with the Caretaker(s).
4) Prototype: get Voyager involved with that conflict a lot more and give us a five-episode story arc. The robots control a large area of space which Voyager has to go through so once they've realized what kind of conflict they are embroiled in, they can't just get away from it but have to fight their way through it.
5) Threshold: have Janeway and Tommyboy's lizard babies grow up fast, which will turn them into some kind of superhuman beings with superhuman abilities and make them confront their parents in a later season. This could have given us our Nothing Human story, for example.
6) Have Kes's abilities manifest themselves a lot earlier on and use them to your advantage. Make a rule about why those abilities are limited so that she can't just get them home in a nanosecond. Get Voyager in a huge conflict with the Dinosaurs from Distant Origin, turn it into a story arc and have Kes play a major role in saving the ship. Preferably major enough to let her stay on the ship.
7) Once Leonardo da Vinci is introduced, have him contribute to more stories than just one. It seems that Seven is open to the whole Leonardo thing so make her work with him and confront Renaissance wisdom with borg philosophy once in a while.
8) Give us three times as many Hirogen stories and explain the past of these people. How come they never settled on a planet but carried on hunting and never saw what the Alpha Hirogen saw (without change they would hunt themselves to extinction)? Now that Janeway is friends with a group of Hirogens, show us that this has led to a conflict within the Hirogen society (does this exist at all?) and because of this a huge conflict is started involving Voyager. This might include Flesh and Blood or might just leave that story intact, in which case it serves as a conclusion to a large story arc spanning four seasons.
9) Throughout Season 4 show us Arturis's people from Hope and Fear and give us some hints how he is planning his revenge on Voyager. These should just be very short, twenty-second scenes, of which the viewer can't make much sense at the beginning but by the time of Hope and Fear, the whole story meshes into a whole.
10) Introduce Janeway's dilemma we see on Night a lot earlier and make it as mysterious as possible. Occasionally the Captain locks herself away in her quarters for days, nobody understands why but most of them suspect foul play. You can even turn this into a mutiny against her and show how the crew react when they find out the truth behind her behaviour.
11) Give the crew of the EQUINOX something to do and get them in a conflict with the Maquis crew from Learning Curve. One group accepts their situation on Voyager, the other not so much. While there's a conflict between them, Voyager gets attacked from the outside as well. How will this turn out? To add even more drama, get the people from Good Shepherd involved somehow and see what happens in a situation which will make them realize they are all in this together and if they don't work together, Voyager's journey will come to an end a lot sooner than expected.
12) Have some recurring villains in seasons 6 and 7 as well. Or if you can't come up with new villains, some of the older ones have joined their forces to start an all-out attack against Voyager. They are very powerful and Voyager is in a difficult situation but with borg modifications, they are not as vulnerable as the enemies originally thought.
Off the top of my head ...