If the map change comes into effect on the 11th of June, like you're assuming, then we can look to the Premier schedule for some hints. The 11th of June would be 4 weeks into the rotation, which means the week 5, 6, and 7 maps (Breeze, Split, and Icebox respectively) are NOT getting rotated out. That leaves only Bind, Lotus, Ascent, and Sunset as the candidates. Sunset is the newest map and Lotus got changes just four months ago, so it's most likely Ascent and Bind getting taken out of the rotation.
As for what's being put in, it's 100% going to be the new map + one other map. If we look at the maps currently out of rotation, the ones that've been out the longest are Pearl and Fracture, so we're most likely getting one of the two back alongside the new map.
TL;DR it's most likely Ascent + Bind OUT, new map + Fracture/Pearl IN.