Spider-Man: Far From Home spoilers ahead. Spider-Man: Far From Home starts soon after the events of Avengers: Endgame, which means this movie has the hard task of explaining how a high school can continue on after half the students disappeared for five years, then came back at the exact same age they were when they left. It also has the task of presenting a Marvel universe without Tony Stark (Robert Downey Jr.). And while it's clear that Peter Parker isn't going to become the new Iron Man in the sense that he'll literally become a different superhero, Far From Home does put Peter (Tom Holland) in Tony Stark's shoes in a different way.
The film shows that Iron Man is well known all around the world, and that he's a hero to everyone. I mean, he did sacrifice his life to bring back the half of all living creatures, so it makes sense that cities around the globe would have giant murals and makeshift tributes on display in his honor.
Peter, however, lost someone much closer to him, as a superhero mentor and a father figure. And one major theme of the film is the mourning period that he personally is going through. When Peter receives the E.D.I.T.H. glasses that Tony left him (the ones that basically control every piece of technology made by Stark Industries), he's quick to give them away to Quentin Beck/Mysterio (Jake Gyllenhaal), because he doesn't feel that he can step into Tony's shoes. Not only does he have insecurities about being a teenager, he also feels like he's not worthy of being a superhero and has just lost another important adult in his life. This movie is truly sad at points.
Thankfully, as Far From Home goes on, Peter regains his confidence and his spidey sense — or "Peter tingle," as Aunt May (Marisa Tomei) calls it — and bonds with Happy Hogan (Jon Favreau) over their shared loss. Happy also introduces Peter to more of Tony's technology, and he takes to it right away. He starts moving around holographic computer screens just like Tony did. And it makes sense: Peter's a nerd, too. He does attend that science and tech high school.
It's unclear where exactly the Marvel Cinematic Universe will go after Far From Home, which closes out Phase 3. There are a number of reported movies: a Black Widow solo movie, Black Panther 2, Guardians of the Galaxy, Vol. 3, among others. But there's isn't any word yet on if or how the different superheroes and remaining Avengers will overlap on screen. An article from Vox suggests that some of the superheroes who more recently joined the MCU will essentially replace the ones who left, like Iron Man and Captain America. It makes sense, because there are some classic superhero personality types and powers that are likely to continue on. "Benedict Cumberbatch’s Doctor Strange (introduced in 2016) has the snarky ego and snappy one-liners of Iron Man," the story puts forth.
But after Far From Home it looks like the "replacement" for Iron Man — at least in one major sense — is Spider-Man. He's inherited Tony's tech and he knows how to use it. That's pretty important.
It's unlikely that Peter will step into Tony's shoes in the sense of being a leader for the Avengers — he still really wants to be a teenager — but with his renewed confidence and fancy, new-to-him technology, he can definitely make his old buddy proud. So rather than being the "new"anyone, he's actually an improved Spider-Man.