Pope Francis calls the priest to formally request of his bishop to continue presiding with the celebration of the 1962 Missal:
Art. 5. Priests who already celebrate according to the Missale Romanum of 1962 should request from the diocesan Bishop the authorization to continue to enjoy this faculty.
This seems clear enough for diocesan priests. What of clergy who serve in religious life? I am sure that religious superiors and local bishops will likely haggle this out in a few places. It seems clear that the bishop is responsible for the overall liturgical life of anyone within the boundaries of the see. How this plays out will get smoothed in some places, and will likely cause consternation in others.
The approved English translation is here.