Hi. They will be moving an existing historical building, Norðurpóll, to Hlemmtorg as part of the 5th phase of construction. The other building, Laugavegur 111, will house a playground "Hlemmur Leikhöll". Unsure whether it's an actual building, but it has an address.

A part of Hlemmtorg after construction of the 5th phase can be seen here:
https://reykjavik.is/sites/default/files/2025-03/hlemmtorg_1.jpg