CoRoT was the first space mission dedicated to exoplanet detection. Operational between 2007 and 2012, this mission discovered 37 transiting planets, including CoRoT-7b, the first terrestrial exoplanet with a measured size. The precision of the published transit ephemeris of most of these planets has been limited by the relative short durations of the CoRoT pointings, which implied a danger that the transits will become unobservable within a few years due to the uncertainty of their future transit epochs. Ground-based follow-up observations of the majority of the CoRoT planets have been published in recent years. Between Dec. 2018 and Jan. 2021, the TESS mission in its sectors 6 and 33 re-observed those CoRoT fields that pointed towards the Galactic anti-center. These data permitted the identification of transits from nine of the CoRoT planets, and the derivation of precise new transit epochs. The main motivation of this study has been to derive precise new ephemerides of the CoRoT planets, in order to keep these planets' transits observable for future generations of telescopes. For large expensive telescopes, this means that transit times should be known with a precision of better than 30 minutes. The TESS data were analyzed for the presence of transits and the epochs of these re-observed transits were measured. The original CoRoT epochs, epochs from ground-based follow-up observations and those from TESS were collected. From these data updated ephemerides are presented for nine transiting planets discovered by the CoRoT mission in its fields pointing towards the Galactic anti-center. In three cases (CoRoT-4b, 19b and 20b), transits that would have been lost for ground observations, due to the large uncertainty in the previous ephemeris, have been recovered. The updated ephemerides permit transit predictions with uncertainties of less than 30 minutes for observations at least until the year 2030. No significant transit timing variations were found in these systems.