From an astrometric point of view, quasars constitute the best and almost ideal reference objects in the celestial sphere, with a priori no significant proper motion. Since the third release of the Large Quasar Astrometric Catalogue (LQAC-3, Cat. J/A+A/583/A75), a large number of quasars have been discovered, in particular those coming from the DR12Q release of the SDSS (Paris et al., 2017, Cat. VII/279). Moreover, for cross-matched objects, we have taken advantage of the very accurate determinations of the quasars identified within the recent Gaia DR1 catalogue (2018, Cat. I/345). Following the same procedure as in the three previous releases of the LQAC, our aim is to compile the large majority of all the quasars recorded so far. Our goal is to record their best coordinates and substantial information concerning their physical properties such as the redshift as well as multi-bands apparent and absolute magnitudes. Emphasis is given to the results of the cross-matches with the Gaia DR1 catalogue. New quasars coming from the DR12Q release were cross-matched with the precedent LQAC-3 compilation with a 1" search radius, in order to add the objects without counterpart to the LQAC-4 compilation. A similar cross-match was done with Gaia DR1 to identify the known quasars detected by Gaia. This enables one to improve significantly the positioning of these objects, and in parallel to study the astrometric performance of the individual catalogues of the LQAC-4 compilation. Finally, a new method was used to determine absolute magnitudes. Our final catalogue, called LQAC-4, contains 443 725 objects. This is roughly 37.82% more than the number of objects recorded in the LQAC-3. Among them, 249071 were found in common with the Gaia DR1, with a 1" search radius. That corresponds to 56.13% of the whole population in the compilation. The LQAC-4 delivers to the astronomical community a nearly complete catalogue of spectroscopically confirmed quasars (including a small proportion of compact AGNs), with the aim of giving their best equatorial coordinates with respect to the ICRF2 and with exhaustive additional information. For more than 50% of the sample, these coordinates come from the very recent Gaia DR1.