Activision has announced that the 2023 Call of Duty League year will be starting as soon as August 22. This doesn't mean we can look forward to more matches and tournaments, but rather that this is when players who are not already under contract for the 2023 season will find themselves as free agents and able to market their services to other franchises.
As has been stated in the roster construction rules post that announced this information, this date has been set to "provide players not under League contracts with the flexibility to sign with any Team in the League" and to "incentivize investment by Team owners in player development within the competitive Call of Duty ecosystem outside of the League".
In terms of when the actual season will start for 2023, that has yet to be announced, but as the new Call of Duty League season usually kicks off early in the New Year, it seems like a fair bet to assume it will be similar this year as well.