https://www.fresnobee.com/news/california/yosemite/article243219776.html

From Facebook:

Following guidance from the White House, Centers for Disease Control and Prevention (CDC), and state and local public health authorities, Yosemite National Park is increasing recreational access. The National Park Service (NPS) is working servicewide with federal, state, and local public health authorities to closely monitor the COVID-19 pandemic and using a phased approach to increase access on a park-by-park basis.

Beginning June 5, Yosemite National Park will reopen access to the Yosemite Wilderness to those with an existing wilderness permit reservation and to those with an existing Half Dome permit.

The health and safety of our visitors, employees, volunteers, and partners continues to be paramount. At Yosemite National Park, our operational approach will be to examine each facility function and service provided to ensure those operations comply with current public health guidance, and will be regularly monitored. We continue to work closely with the NPS Office of Public Health using CDC guidance to ensure public and workspaces are safe and clean for visitors, employees, partners, and volunteers.

While these areas are accessible for visitors to enjoy, a return to full operations will continue to be phased and services may be limited. When recreating, the public should follow local area health orders, practice Leave No Trace principles, avoid crowding and avoid high-risk outdoor activities.

The CDC has offered guidance to help people recreating in parks and open spaces prevent the spread of infectious diseases. We will continue to monitor all park functions to ensure that visitors adhere to CDC guidance for mitigating risks associated with the transmission of COVID-19, and take any additional steps necessary to protect public health.

Check https://go.nps.gov/covid for updates.

From a comment on the post announcing the June 5th reopening on the Yosemite Facebook page. The Yosemite Conservancy wilderness permits request page confirms it.

"Dear Yosemite Employees,
Following guidance from the White House, Centers for Disease Control and Prevention (CDC), and state and local public health authorities, Yosemite National Park is increasing recreational access. Beginning June 5, Yosemite National Park will reopen access to the Yosemite Wilderness to those with an existing wilderness permit reservation and to those with an existing Half Dome permit. Glacier Point Road will be open, but Tioga Road will remain closed until further notice. Permitholders (and others authorized to enter the park) may enter and exit the park between 5 am and 11 pm.
Wilderness Permits
Normally, 60% of wilderness permits are available by reservation 24 weeks in advance, with the remaining 40% available in-person the day before the hiking start date. Wilderness centers will not be issuing permits in person this year.
This year, 40% of permits that would normally be available first-come, first-served are instead available by lottery two weeks in advance. Beginning June 11, you can submit a reservation request 15 days in advance of a hike, with the lottery running 14 days in advance. Unreserved permits remain available up to nine days in advance. It is not possible to obtain a wilderness permit reservation fewer than nine days in advance.
For hiking start dates from June 11 to June 25, any unreserved permits that are part of the 60% quota are available at https://yosemite.org/yosemite-wilderness-permit-request.../
All permits will be emailed to reservation holders, following required permit education from wilderness rangers.
Half Dome Permits
Half Dome permits for June 5 and later that were awarded during the preseason lottery are valid. The daily lottery is not resuming immediately, but may resume later this month."