The Keeping Time quest can be gotten from Osiris at The Sundial on Mercury after you have completed the Matter of Time quest. This quest requires you to get the Mars: Obelisk Attunement quest as well. If you cannot get this from Osiris, grab the available quests, exit it out, then interact with him again, and it should fix the issue.
Step 1 – Mars: Obelisk Attunement
For the first step, you need to finish the Mars: Obelisk Attunement quest. You need to collect 50 Salvaged BrayTech from Hive enemies on Mars. This task is easy to do. There is a vast amount of Hive that spawn in the area. There is also a good chance that people will be taking part in the Escalation Protocol, making it even easier to do.
Once you have all 50, go to the Obelisk near the BrayTech spawn point, and interact with it.
Step 2 – Mars: Light Collection
You have repaired and modified the Obelisk. Now, you need to collect Light. Similar to the first Obelisk, you need to kill enemies with your abilities or your Super to collect Orbs of light. Equip a Masterworked weapon or two to ensure plenty more drop, then kill every enemy you can find. Keep using abilities and Supers to get your kills until you reach 100 percent.
After, return to the Obelisk to activate it and to link it to the Sundial.
Step 3 – Time Lost And Found
For this step, you need to complete three Timelost Weapon Bounties. You can get these from Obelisks that are Resonance rank Level 1. You will need 10 Polarized Fractaline, and 3000 Glimmer, to get one. Each Obelisk has three Timelost Weapon Bounties that become available at Resonance Rank 1, 3, and 5.
Fortunately, for this quest step, you can do the first level bounty three times to progress.
Step 4 – Crisis Averted
You can now return to Osiris at the Sundial on Mercury to hand in the quest.