Star Trek Discovery: Every Easter Egg & Hidden Reference From 'People Of Earth'

Speaking of quadrants...

Later in the episode Michael tells Book he has a fresh start in a whole new quadrant now, which confirms that Hima (as seen in “That Hope is You”) was definitely not in the Alpha Quadrant.

However, Michael also says she and Book had some kind of adventure at Donatu VII, a planet which must reside in the same system as Donatu V, previously the site of a battle between the Federation and the Klingons as mentioned in “The Trouble with Tribbles."

According to Star Trek: Star Charts (a book which Star Trek: Discovery often uses for background material), Donatu V was located in the Beta Quadrant, so it seems likely that Book and Michael’s exploits (as well as Hima) were located in the Beta Quadrant.