The Additional Representative Images for Legacy (ARI-L) project is a European Development project for ALMA Upgrade approved by the Joint ALMA Observatory (JAO) and the European Southern Observatory (ESO), started in June 2019. It aims to increase the legacy value of the ALMA Science Archive (ASA) by bringing the reduction level of ALMA data from Cycles 2-4 close to that of data from more recent Cycles processed for imaging with the ALMA Pipeline. As of mid-2021 more than 150000 images have been returned to the ASA for public use. At its completion in 2022, the project will have provided enhanced products for at least 70% of the observational data from Cycles 2-4 processable with the ALMA Pipeline. In this paper we present the project rationale, its implementation, and the new opportunities offered to ASA users by the ARI-L products. The ARI-L cubes and images complement the much limited number of archival image products generated during the data quality assurance stages (QA2), which cover only a small fraction of the available data for those Cycles. ARI-L imaging products are highly relevant for many science cases and significantly enhance the possibilities for exploiting archival data. Indeed, ARI-L products facilitate archive access and data usage for science purposes even for non-expert data miners, provide a homogeneous view of all data for better dataset comparisons and download selections, make the archive more accessible to visualization and analysis tools, and enable the generation of preview images and plots similar to those possible for subsequent Cycles.