Yesterday the news arrived at this site that from now on the Pilgrim’s Office will issue a total of 60 diamoniterion’s a day to pilgrims and up to 20 visitors and pilgrims per day will be allowed to visit each monastery, 15 for each cenobitic skete. Additionally, travel between monasteries on Mount Athos is allowed again.
Each visitor must still confirm his stay with the monastery that will host him. From last Wednesday 1 of July the Greek borders are open again to 15 EU countries, that are considered save epidemiologically. Russian pilgrims are not allowed to enter Greece until now.
For older information about the lockdown Athos have look here.

On the site of orthoxianewsagency.gr I also read that the number of visitors to Athos increased the past years with 30% and numbers 250.000 to 270.000 visitors each year. The increased traffic is mainly caused by Bulgarian and Serbian pilgrims, who filled the gap left by the Russians.
Wim Voogd, 4-7-2020