The CW published its schedule for January 2021.
Sunday
8 PM: Batwoman
9 PM: Charmed (new time slot)
Monday:
8 PM: All American
9 PM: Black Lightning
Tuesday:
8 PM: The Flash
9 PM: Superman & Lois (new drama)
Wednesday:
8 PM: Riverdale
9 PM: Nancy Drew
Thursday:
8 PM: Walker (new drama)
9 PM: Legacies
Friday:
8 PM: Penn & Teller: Fool Us (new time slot)
9 PM: Whose Line Is It Anyway? (new time slot)
9:30 PM: Whose Line Is It Anyway? encores
8 PM: Batwoman
9 PM: Charmed (new time slot)
Monday:
8 PM: All American
9 PM: Black Lightning
Tuesday:
8 PM: The Flash
9 PM: Superman & Lois (new drama)
Wednesday:
8 PM: Riverdale
9 PM: Nancy Drew
Thursday:
8 PM: Walker (new drama)
9 PM: Legacies
Friday:
8 PM: Penn & Teller: Fool Us (new time slot)
9 PM: Whose Line Is It Anyway? (new time slot)
9:30 PM: Whose Line Is It Anyway? encores

They also shared the new "season 16" (or 15 part 2) promotional pic:
The final 7 episodes are coming this fall to The CW! #SPNFamilyForever pic.twitter.com/CJS1m8vxGk
— Supernatural (@cw_spn) May 14, 2020
At the same time, The CW announced Jared Padalecki's new series Walker is set to premier in January.

Walker's promotional photo was also released!
#Walker is coming January 2021 to The CW! pic.twitter.com/CBGgzS61SN
— Walker (@thecwwalker) May 14, 2020
Entertainment Weekly also covered the news: The CW pushes return of its shows to 2021, except Supernatural
Breaking in my ninja jeans https://t.co/MjNlyftqSS
— Jared Padalecki (@jarpad) May 14, 2020
So we will see the ending of Supernatural before beginning our new journey with Jared on Walker!
We will update as more information becomes available.
We will update as more information becomes available.