This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
In 2268, a red light on Pavel Chekov's board signaled that either a hatch or a vent was not secured. Before the dikironium cloud creature entered the USS Enterprise, there was a red light for a open hatch on the number two impulse engine. (TOS: "Obsession")
In 2371, Julian Bashir cautioned Kira Nerys not to replace the carpets in Deep Space 9's guest quarters for the visiting Yalosian ambassador with anything red or orange, as they didn't see that part of the color spectrum. (DS9: "Improbable Cause")
Young Annika Hansen's favorite color was red. In 2374, as a liberated Borg drone, Seven of Nine, she told Captain Kathryn Janeway this after Janeway had earlier mentioned Hansen's favorite color as being one of the things they didn't know about her yet. (VOY: "The Gift")
In the 32nd century, the holographic bird alarm clock owned by Aditya Sahil would change its color daily, with red being one of the colors. In 3188, Michael Burnham described her friend Sylvia Tilly as having red hair. (DIS: "That Hope Is You, Part 1")