In the context of developing the circular economy that enables a more sustainable use of the available resources and minimum waste generation, marine macroalgae have attracted the attention of researchers and industry due to its potential as a renewable resource. The current work aims to contribute to the design of a complete biorefinery processing, using Fucus spiralis seaweed (brown division) as starting material, and to determine the potential of the derived waste as biosorbent of heavy metals in aqueous solution. The macroalgae waste was obtained after the sequential separation of polyphenols, fucoidan and alginate extracts from F. spiralis. The capacity of F. spiralis waste for Pb(II) removal was successfully tested through biosorption tests. The uptake of Pb(II) was found to be very fast (few hours to achieve equilibrium). Tests performed with an initial metal concentration of 20 mg/L established the best adsorbent dosage (0.50 g/L) and an optimum pH of 4.5. In these conditions, lead was almost completely removed from the aqueous solution. Maximum adsorption capacity predicted by Langmuir model was 132 ± 14 mg/g (pH 4.5 ± 0.5, 20 °C). Desorption studies were conducted with different possible eluents. The best results were obtained with EDTA 0.1 mol/L, generating a 95 ± 4% desorption. F. spiralis biomass can therefore be submitted to a complete biorefinery processing and design in the attempt to fulfil the “zero-waste” concept.