I'm well into the third act of my novel and I'm introducing a new character that will play a part in the ending and an even bigger part in the roughly sketched sequel I have in mind.
Now, I'm pretty sure I've read somewhere that you shouldn't introduce new characters so late, unless not if you haven't foreshadowed them before. I'm wondering then if this is an hard limit, or there are exceptions to be made.
If a character appears in the third act and helps solve a major problem the main characters have carried for the two previous acts, that character is sort of deus ex machina - something previously entirely unforeseen comes and solves the problem.
If a character appears in the third act and makes new problems for the main characters, that's diabolus ex machina. It can still feel unfair, but it is tolerated better. The character presents an extra challenge, rather than an unearned solution.
If the character appears in the third act and does neither of the above, but instead serves as "setting", or helps resolve a minor problem that only appeared in the third act, there is no problem that I can see.
But if you need a particular character to have a major impact on the story, why not foreshadow their existence before? Drop hints in earlier chapters that there's someone named X, or someone who has been rumoured to do Y, problem solved.
As an example, the whole Return of the King can be treated as the 3rd act of The Lord of the Rings. What characters do we meet there for the first time? There's Denethor - a major actor. We knew of him, of course, ever since we met Boromir. Gwaihir the Windlord, often considered a (minor) deus-ex-machina - he too was mentioned back in act 1, having rescued Gandalf from Isengard. There's Beregond and his son Bergil. They are not actors on the stage - they serve to introduce Pippin and the reader to the new setting. There is Dernhelm, who turns out to be Eowyn, there are named commanders of the Rohirrim and of Gondor who are parts of the setting - again, they don't act to affect the story. There is Ghân-buri-Ghân and there is Ioreth the healer - they solve relatively small problems that are part of the course of the 3rd act's story. And there's Rose, who has been Sam's love interest all along, only she hasn't been mentioned until the last chapters of the novel.
All the above examples, save the very last one, fall into two categories: either they are actors with an important role, and their presence has been adequately foreshadowed; or they are non-actors, but rather named parts of the setting. Since they do not affect anything, there's no need to introduce them in advance. The only exception is Rose, who reads like Tolkien's afterthought, and should really have been introduced earlier.
I see 2 options to hint at a 3rd-Act character before they are introduced. Both ways prep the reader that there is a coming "component" to the story, like a Chekov's gun. The hints can be overt, like they are actually seeking this person, or subtle with their "presence" being felt long before they are introduced.
A little foreshadowing, even if it turns out to be "wrong", will help this character not be a deus ex machina. Their introduction can still sideline the characters, but for the reader they do not emerge completely from nowhere. Readers have a partial awareness this person exists, but they are an abstract (like the Wizard of Oz) who turns out to be nothing close to what was expected, or they have been feeling his effects (positive or negative) before they become aware it is all due to this surprise person they weren't aware of. Once they realize it is a person, they may not need to look very far to find him.
If you are not going to rush into telling his/her story line, and slowly allow the reader to get used to the new person, I can't see how it will be a big deal. It's your story, you are the creator, and you can do whatever you want with it.
But yes, it is better to introduce him/her a bit earlier, as then you will have more time for describing him/her at a comfortable pace.
