This study aims at assessing the use of a novel damper, which is called the Prestressed LEad Damper with Straight Shaft (or PS-LED), for the seismic rehabilitation of RC framed buildings. This device provides high energy dissipation by the friction activated between a lead core and a shaft and achieves a high specific output force by preloading the lead during the assembly. In order to show the effectiveness of the PS-LED device for the retrofit of existing buildings, a RC structure designed according to past codes that ignored seismic actions is retrofitted with the PS-LED system considering two different damage targets: (i) in the first case, the structure is retrofitted in order to behave elastically under the design earthquake; (ii) in the second case, a partially dissipative behavior of the structure is conceived, with activation of plastic hinges, and limited and reparable damage. In order to assess the suitability of the design procedure, non-linear static analyses are performed on the upgraded building, showing a satisfactory agreement between the seismic performance and the design target. Non-linear dynamic analyses are further carried out considering a suite of bidirectional artificial ground motions with response spectra matching on average the target spectrum according to the Italian Building Code for the life-safety limit state. Finally, a comparison is performed between the performances of the building retrofitted with the PS-LED device and the building retrofitted with a conventional steel hysteretic damper (SHD), demonstrating that the PS-LED, thanks to its superior damping capacity, limits the increase in internal forces that usually affects frames equipped with SHDs, reducing the need of local strengthening of the columns and foundations and consequently the total cost of the seismic rehabilitation.