When Does "Star Trek: Discovery" Season Two (2019) Take Place?
"Star Trek: Discovery" season two is a science fiction television series showran by Gretchen J. Berg with Aaron Harberts and Alex Kurtzman that premiered January 17th, 2019. So when is "Star Trek: Discovery" season 2 set? 
 
 It takes place on the fictional Star Trek timeline in the year:
It takes place on the fictional Star Trek timeline in the year: 
 
We know this because season 2 episode 1 "Brother" begins moments after the end of season 1 episode 15 "Will You Take My Hand?" (2018), which takes place in 2257 AD.

2257 AD - 2258 AD
We know this because season 2 episode 1 "Brother" begins moments after the end of season 1 episode 15 "Will You Take My Hand?" (2018), which takes place in 2257 AD.
Later, season 2 episode 14 "Such Sweet Sorrow, Part 2" includes an epilogue that seems to take place 124 days later that the rest of the episode. That would make it early 2258 AD. 
124 days = 4 months 
and 
. 
 
Although the famous "stardate XXXX.X" captain's records that open most episodes and some films were mistaken for years on the Gregorian calendar, there is no one-to-one relationship between them. As identified in the biography "Gene Roddenberry: The Myth and the Man Behind Star Trek": "They marked off sections on a pictorial depiction of the known universe and extrapolated how much earth time would elapse when traveling between given points, taking into account that the Enterprise's warp engines would be violating Einstein's theory that nothing could exceed the speed of light. They concluded that the 'time continuum' would therefore vary from place to place, and that earth time may actually be lost in travel. 'So the stardate on Earth would be one thing, but the stardate on Alpha Centauri would be different,' Peeples says." so they are relative to long distance travel and not an absolute calendar. HOWEVER, actual years on the Gregorian calendar began to be used later. 
This StarTrekLitVerse.com page makes an exhaustive attempt to track how much time passes in seasons 1 and 2 of the show. 
It is the second chronological TV show in the Star Trek universe and can be watched at its timeline point. 

