This study aimed to investigate the effects of using olive oil (OO) in a partial replacement of fish oil (FO), with or without supplementation with rosemary essential oil (RO), on the growth performances and flesh quality traits of farmed Dicentrarchus labrax. Sea bass were fed with the experimental diets for 200 days; afterwards, they were caught and stored in ice (0–2 °C) for up to 17 days. The specific growth rate (SGR) and feed conversion rate (FCR) were calculated. Fillets were analyzed for physical features, chemical composition, fatty acid profile, and malondialdehyde (MDA) concentration on days 0, 5, 10, and 17 of storage. The fillets were assessed for sensory properties according to the QIM and Torry Scheme methods. No statistical differences between groups were found for the final average body weight, SGR, FCR and the flesh chemical composition. Supplementation with RO reduced (p < 0.05) MDA concentration, thus improving the shelf life of fish by up to 10 days. The sensory score (QIM) increased linearly (p < 0.05) with storage time; for cooked fillet, the Torry Scheme score decreased (p < 0.05) with storage time. The economic analysis of feed cost has proven the feasibility of using olive oil as local feed ingredient in the partial replacement of fish oil.