Fish processing industries generate a large volume of discards. In order to fulfil with the principles of a sustainable circular economy, it is necessary to maintain aquaculture by-products in the food chain through the production of high-value biomolecules that can be used as novel ingredients. In this study, we try to give value to the gilthead sea bream by-products, evaluating the composition and the nutritional value of the muscle and six discards commonly obtained from the fish processing industry (fishbone, gills, guts, heads, liver, and skin), which represent ≈ 61% of the whole fish. Significant differences were detected among muscle and by-products for fatty acid and amino acid profile, as well as mineral content. The discards studied were rich in protein (10%–25%), showing skin and fishbone to have the highest contents. The amino acid profile reflected the high quality of its protein, with 41%–49% being essential amino acids—lysine, leucine, and arginine were the most abundant amino acids. Guts, liver, and skin were the fattiest by-products (25%–35%). High contents of polyunsaturated fatty acids (PUFAs) (31%–34%), n-3 fatty acids (12%–14%), and eicosapentaenoic acid (EPA) + docosahexaenoic acid (DHA) (6%–8%) characterized these discards. The head displayed by far the highest ash content (9.14%), which was reflected in the mineral content, especially in calcium and phosphorous. These results revealed that gilthead sea bream by-products can be used as source of value-added products such as protein, oils, and mineral supplements.