The Timekeepers were a subsect of the Followers of Kahless, an order of Klingon monks who resided within the monastery to Kahless the Unforgettable on Boreth. Their purpose was specifically to protect the time crystals contained within the monastery. To most Klingons, time crystals (poH qut in Klingonese) were a myth, a symbol of Kahless and the namesake of Qo'noS, but the Timekeepers understood their true power and sought to protect them. In 2257, they were led by Tenavik, son of Voq and L'Rell, who had arrived at the monastery as an infant, but was a grown man months later due to exposure to the crystals. (DIS: "Through the Valley of Shadows")
In an alternate timeline, the Timekeepers allowed Rear Admiral Christopher Pike to travel back to 2259 with a time crystal to stop his younger self from trying to alter his fate, as it would have catastrophic consequences on the galaxy. Admiral Pike was able to convince the Klingons that he would not put his own fate ahead of that of the galaxy, which is why they allowed him to show the Pike of 2259 the consequences of his decision, rather than simply kill him. (SNW: "A Quality of Mercy")