Hawkeye is looking to be one of the most faithful adaptions from Marvel Studios, specifically from Matt Fraction's Hawkeye, a comic run that lasted for 22 issues from 2012 to 2015. It was most famous for solidifying the relationship between Clint Barton and Kate Bishop, reintroducing Barton's deafness that was cured decades before, and introducing the lovable pizza-loving dog, Lucky.
From what has been gleaned from set photos, Hawkeye will be taking an enormous influence from Fraction's comic run. Not only will the show likely adapt one of the most amusing action scenes from the original comic, but it will be pinning Clint and Kate against the Tracksuit Mafia, who have the amusing character trait of using “bro” as if the word it belongs to them.
So, it isn't a surprise then that new set photos from Hawkeye continue to flaunt its greatest influence by showing Clint and Kate wearing some nice formal wear.
Two of these photos seem to be them on break, as Renner is wearing glasses while he appreciates Steinfeld's own dog:
The second set of photos shows Renner and Steinfeld filming a panning shoot, still dressed fancy, as they seem to be exchanging dialogue and seemingly arriving somewhere:
Finally, these photos give a better look at what Renner and Steinfeld are wearing, which seems to be a straight forward tuxedo for Clint Barton and a dress under Kate Bishop's coat, although it seems like she's wearing boots as well:
WHAT THIS MEANS
In the Matt Fraction comic run, Clint Barton and Kate Bishop crash the opening of the world's first six-star hotel, believing that it'll be hit by criminals or villains. Just like the comics, Renner is wearing a tuxedo, complete with a restraining bow tie, but Steinfeld's outfit is far more subtle than her comic counterpart, who was decked out in purple.
Specifically, they're attending a performance that harkens back to Clint Barton's time in the circus, but in the audience with them are dozens of criminals and supervillains including Wilson Fisk and Madame Masque. When the performance is revealed to be a cover to steal from everyone blind, Clint and Kate get to work, running around and ruining their expensive (or rented) dress clothes.
However, one big link that this event could have with the show is that the villain in this issue is connected to Jack Duquesne, a.k.a. Swordsman. Tony Dalton, known for his work on Better Call Saul, was recently cast as Swordsman, so it is very likely that this event, or at least the setup, will be adapted into the show in some way.