Zelda is absolutely poorly represented in Smash for being presented as a series equal to Mario in most promotional material, including Smash.
Firstly, every fighter is just a version of one of the Triforce holders. And it's not bad to have them all. Gotta have all three members... Shiek is alright, very distinct from Zelda. I don't even mind that there's three Links. One of my favorite things about Link is just how different he can be from game to game. If anything I think we could stand to have yet another version of Ganon. Ganondorf has always been poorly represented in Smash, and although he's getting better, he's still not a very good representation of the series main big bad. Which is exactly why I propose Pig Ganon, styled after the more classic blue trident weilding pig. To be honest i'm surprised he doesn't have as much support as K. Rool and Ridley. Being okay with just Ganondorf strikes me as being okay with just having Bowser Junior but no actual Bowser.
While i'm still on the topic of Triforce Holders, I did have the idea for another version of Link.... but I think three Links is enough. Four would be excessive. In the event that Young Link didn't return, I would say we should have Classic Link. The first Link that isn't a clone of the others. He would mainly use tools that the other Links don't like the hammer and the bug net, or tools that are 2D exclusive like the magic rod, the candle, pegasus boots, and possibly a few spells from Zelda 2 like fire, reflect, ect... but this one will never happen, it was just for funsies.
Outside of the triforce weilders, there are still plenty of Zelda characters to choose from with great importance. In my opinion, the priority should go to characters who have also reincarnated or appeared in multiple games accross the series just like the Triforce holders. But that doesn't mean that there aren't one off Zelda characters that are just as deserving, if not, more so, than series regulars.
A lot of people aren't going to want to hear this, but outside of pig Ganon, in my opinion, the MOST deserving Zelda character for Smash Bros has to be Tingle. He's one of the Zelda characteres that has gotten the chance to appear not only across multiple games but appear in different eras of the series, and he's the ONLY Zelda character to have the honor of having his own series of games. He also represents the much more silly and weird side of the Zelda series that a lot of fans seem to forget about or look the other way on. Zelda is by no means a completely serious series, and Tingle is far from the only aspect of the weird parts, but he sure as heck embodies it. Were he to make it into the series, I'd expect him to take on his Rosy Rupeeland appearance. It's different enough from his Majora's Mask incarnation, that I don't think the Great Bay cameo would be an issue.
Aside from that, you've got Impa, the only Zelda character who's as old as the triforce holders. She may not have appeared until Ocarina of Time, but she's been a part of the Zelda series lore since the original NES game. Sometimes she's depicted as an elderly woman, sometimes a young ninja warrior, in Skyward Sword, she was both, and in the Oracles games, she was a huge tree trunk armed mountain of a woman. She's got potential to be Shiek echo, semi-clone, or even her own character.
Skull Kid just barely qualifies for being a recurring character on account of being in Ocarina of Time and Twilight Princess, but his most prominent role is what really skyrockets him to the same status as Impa and Tingle. I don't really need to say much about the Majora's Mask incarnation, we all know about him at this point, and how the mask he wears is easily the most recognizable thing in Zelda right behind the Triforce, still being sold on merchandise to this day.
Vaati the wind mage is a strange one. He only had one truly notable appearance in Minish Cap, where he looked like some sort of dark foil to Link, but with more magical abilities. This is the form everybody supports for Smash. But he was also the main antagonist of the two Four Swords games, where he only appeared as a flying eyeball monster. He's lost a lot of support over the years, but I still think he'd make a good addition... but he's not quite so notable as some of the one off characters.
The only other recurring character I think could qualify is a bit of a stretch. A duo of characters. Malon and Epona. Epona. Epona is definitely the more famous of the two, appearing in Ocarina of Time, Majora's Mask, Four Swords Adventures, Twilight Princess, Minish Cap, and Breath of the Wild. Malon has appeared in all of those games but TP and BotW, but she did appear in Oracle of Seasons. I don't see this one happening. But I feel like their star status should be enough to say they're not entirely undeserving.
A case could be made for Tetra. I'd certainly rather have her than Toon Zelda. But something tells me neither of them are very likely, even if Toon Zelda was initially planned. You could maybe even go with Linebeck, but I don't see that one happening either.
Last one from this category that I think people are sleeping on is Twinrova. The only boss that speaks to you in Ocarina of Time, surrogat mothers to Ganondorf, NPCs in Majora's Mask, and major antagonists of the Oracle of Seasons and Ages true ending. I don't think she has enough support from anyone, but I feel like she's deserving enough.
And here we have the one offs. Characters that appeared in one game, but they were such break out stars that they're essentially the faces of their respective games. And with the Zelda series characters in Ultimate being made up of incarnations from accross the series instead of one game like past titles, there's never been a better time to invite the one-offs.
You've got Midna, alas, she's been relegated to Assist Trophy again. But even so, I don't think there's a single side character in the series that resonated with fans like she has. She does still have a chance at possibly being a Zelda echo in her Twili Form, but to be frank, I would not be happy with that. I'm not a fan of her Twili Form, and she's more famously known as a mischeivious, wolf riding imp with a giant hand coming out of her head. That, and I believe the most likely Zelda Echo will be Hilda from a Link Between Worlds. Maybe Midna will get her chance another day.
You've got Girahim, while i'm not the biggest fan of the game he comes from, he's easily one of the most fun villains in a Zelda game in a long time, Nothing at all like the villains from previous games, and much more actively antagonistic too... he too has unfortunately become an assist trophy. But he's still earned his status as a potential character.
I occasionally see support for the Champions of Hyrule, but i'm going to be real, I don't think any of those characters are that great in comparison to their competition, and it seems unrealistic to expect all four of them, and it would be pointless to only have one of them.
Some of the runner ups in this category would be Zant, Ravio, Yuga, any of Link's transformations from Majora's Mask, any of the Ocarina of Time sages ( minus Raru ), King Daphnes, Demise, and Malon. All great characters that have their fans, but they probably don't quite have the star power that they would need.