The mechanical recycling of thermoplastics (especially of polyolefins) often results in recyclates with inferior properties compared to their virgin counterparts. This phenomenon is mainly due to the modification of the polymer microstructure induced by the degradation processes undergone by the materials during their service life and reprocessing. In this work, a promising route for obtaining high-melt-strength recycled high-density polyethylene (HDPE) is proposed. In particular, the exploited approach involves the utilization of a commercially available additive (i.e., Nexamite