With the target of recovering rare earth elements (REEs) from acidic leachates, a new functionalized hydrogel was designed, based on the phosphorylation of algal/polyethyleneimine beads. The functionalization strongly increased the sorption efficiency of the raw material for Pr(III) and Tm(III). Diverse techniques were used for characterizing this new material and correlating the sorption performances and mechanisms to the physicochemical structure of the sorbent. First, the work characterized the sorption properties from synthetic solutions with the usual procedures (study of pH effect, uptake kinetics, sorption isotherms, metal desorption and sorbent recycling, and selectivity from multi-element solutions). Optimum pH was found close to 5; sorption isotherms were fitted by the Langmuir equation (maximum sorption capacities close to 2.14 mmol Pr g−1 and 1.57 mmol Tm g−1). Fast uptake kinetics were modeled by the pseudo-second order rate equation. The sorbent was highly selective for REEs against alkali-earth and base metals. The sorbent was remarkably stable for sorption and desorption operation (using 0.2 M HCl/0.5 M CaCl2 solutions). The sorbent was successfully applied to the leachates of Egyptian ore (pug leaching) after a series of pre-treatments (precipitation steps), sorption, and elution. The selective precipitation of REEs using oxalic acid allows for the recovery of a pure REE precipitate.