Context. The New Astrometric Reduction of Old Observations (NAROO) program is dedicated to the measurement of astrophotographic plates and the analysis of old observations for scientific purposes. One of the objectives of the NAROO program is to provide accurate positional measurements of small Solar System bodies in order to improve our knowledge of their orbits and dynamics. Aims. Focused on potentially hazardous asteroids (PHAs), which are near-Earth asteroids (NEAs) making very close encounters with the Earth, this paper aims to emphasize the value of old photographic plate observations. As they provide accurate astrometric measurements over a large time interval, such observations are essential to determine reliable orbits and to detect small accelerations, such as the Yarkovsky effect. Methods. Photographic plates consist of a substantial source of old observations of Solar System objects. From existing databases, we identified old and precovery observations of PHAs, which are fortuitous observations made before their discovery. We used the NAROO machine to digitize the plates, and we performed the astrometric reduction with the Gaia DR3 reference star catalog. We added the results to the observation dataset of PHAs in order to determine new orbital solutions and possibly detect the Yarkovsky effect with the Numerical Integration of the Motion of an Asteroid (NIMA) program. In addition, we considered a possible timing error in the orbit adjustment, which is generally not taken into account in such problems, and show its influence. Results. We were able to find precovery observations of PHAs in photographic plate databases. Their introduction in the dataset show a significant improvement of the accuracy of the new orbital solutions. They also help in detecting and measuring the Yarkovsky effect and improve its accuracy. Hence, we demonstrate the interest of the reduction or new reduction of old photographic plates for the orbit determination of PHAs.