As Harberts noted, the crew of the Discovery did, indeed, run into the Enterprise at the very end of the Season 1 finale, when everyone’s favorite Original Series starship sent a distress call that was intercepted by the Discovery.
Obviously, it would follow that Season 2 would see at least some members of the two crews meet, and unless everyone aboard the Enterprise is naked, we should be seeing those happy, shiny OG uniforms.
Gretchen J. Berg and Aaron Harberts were asked about the possibility of those iconic TOS Starfleet uniforms showing up during the next season of Discovery during a panel at WonderCon 2018 (via ComicBook.com), and while they were a bit cagey in their response, it does sound like there’s a good chance that we can see the old school Starfleet uniforms make an appearance on the show in Season 2.