Context. The INvestigating Stellar Population In RElics (INSPIRE) is an ongoing project targeting 52 ultra-compact massive galaxies at 0.1 < z < 0.5 with the X-shooter at VLT spectrograph (XSH). These objects are the ideal candidates to be 'relics', massive red nuggets that have formed at high redshift (z > 2) through a short and intense star formation burst, and then have evolved passively and undisturbed until the present day. Relics provide a unique opportunity to study the mechanisms of star formation at high-z. Aims.INSPIRE is designed to spectroscopically confirm and fully characterise a large sample of relics, computing their number density in the redshift window 0.1 < z < 0.5 for the first time, thus providing a benchmark for cosmological galaxy formation simulations. In this paper, we present the INSPIRE Data Release (DR1), comprising 19 systems with observations completed in 2020. Methods. We use the methods already presented in the INSPIRE Pilot, but revisiting the 1D spectral extraction. For the 19 systems studied here, we obtain an estimate of the stellar velocity dispersion, fitting the two XSH arms (UVB and VIS) separately at their original spectral resolution to two spectra extracted in different ways. We estimate [Mg/Fe] abundances via line-index strength and mass-weighted integrated stellar ages and metallicities with full spectral fitting on the combined (UVB+VIS) spectrum. Results. For each system, different estimates of the velocity dispersion always agree within the errors. Spectroscopic ages are very old for 13/19 galaxies, in agreement with the photometric ones, and metallicities are almost always (18/19) super-solar, confirming the mass-metallicity relation. The [Mg/Fe] ratio is also larger than solar for the great majority of the galaxies, as expected. We find that ten objects formed more than 75% of their stellar mass (M∗) within 3 Gyr from the big bang and classify them as relics. Among these, we identify four galaxies that had already fully assembled their M∗ by that time and are therefore 'extreme relics' of the ancient Universe. Interestingly, relics, overall, have a larger [Mg/Fe] and a more metal-rich stellar population. They also have larger integrated velocity dispersion values compared to non-relics (both ultra-compact and normal-size) of similar stellar mass. Conclusions. The INSPIRE DR1 catalogue of ten known relics is the largest publicly available collection, augmenting the total number of confirmed relics by a factor of 3.3, and also enlarging the redshift window. The resulting lower limit for the number density of relics at 0.17 < z < 0.39 is ρ ∼ 9.1 × 10-8 Mpc-3.