With the release of the leaked Avengers: Infinity War trailer and the new Avengers: Infinity War poster, it's revealed that Peter Paker does accept the new Iron Spider(?) costume that Tony Stark attempted to give him near the end of Spider-Man: Homecoming.
It is unknown if it's technically the "Iron Spider" costume from the comics, but maybe it's called The Avengers: Infinity War Spider-Man costume.
Either way, an official image has hit the net. Check it out:
Update: I photoshopped a pic of the costume to make it brighter. See below.
Update #2: The Marvel artist responsible for the design, Ryan Meinerding, confirms there is no blue color in the suit.
Spoiler alert! Sorry if you haven't seen Spider-Man: Homecoming yet! They officially released a still of the third Spidey suit that shows up in the movie. It was fun to work on a design that didn't have any blue for once! This weekend at SDCC I was hearing a lot of love for the homemade suit. Which one was your favorite? #spidermanhomecoming #spiderman #spidey #moviestill #marvelstudios #marvel #comics #marvelcinematicuniverse #costumedesign
Photoshopped to make brighter and add color:
The Avengers: Infinity War hits May 4, 2018 directed by Joe and Anthony Russo starring Josh Brolin as Thanos, Robert Downey Jr. as Tony Stark/Iron Man, Chris Pratt as Star-Lord, Tom Holland as Peter Parker/Spider-Man, Chris Evans, Chris Hemsworth, Mark Ruffalo, Scarlett Johansson, Jeremy Renner, Sebastian Stan, Zoe Saldana, Karen Gillan, Dave Bautista, Bradley Cooper, Vin Diesel, Elizabeth Olsen, Paul Bettany, Chadwick Boseman, Benedict Cumberbatch and Benedict Wong.
As the Avengers and their allies have continued to protect the world from threats too large for any one hero to handle, a new danger has emerged from the cosmic shadows: Thanos. A despot of intergalactic infamy, his goal is to collect all six Infinity Stones, artifacts of unimaginable power, and use them to inflict his twisted will on all of reality. Everything the Avengers have fought for has led up to this moment - the fate of Earth and existence itself has never been more uncertain.