CBS is already producing new Star Trek shows, starting with this spin-off to "Star Trek: Discovery (2017-)":

'Star Trek: Short Treks' Episode 1 Packs a Lot into 15 Minutes

The First Episode of Short Treks Feels Like a Star Trek B-Plot in the Best Possible Way

Trailers

Star Trek Short Treks Promo

Star Trek Short Treks "Runaway" Promo

Episodes and airdates

• S1E01 "Runaway"                                  4 October 2018

• S1E02 "Calypso"                                     8 November 2018

• S1E03 "The Brightest Star"                 6 December 2018

• S1E04 "The Escape Artist"                  3 January 2018