Context. Statistical analyses based on Kepler data show that most of the early-type M dwarfs host multi-planet systems consisting of Earth to sub-Neptune sized planets with orbital periods up to ∼250 days, and that at least one such planet is likely located within the habitable zone. M dwarfs are therefore primary targets to search for potentially habitable planets in the solar neighbourhood. Aims. We investigated the presence of planetary companions around the nearby (7.6 pc) and bright (V = 9 mag) early-type M dwarf Gl 514, analysing 540 radial velocities collected over nearly 25 years with the HIRES, HARPS, and CARMENES spectrographs. Methods. The data are affected by time-correlated signals at the level of 2-3 m s −1 due to stellar activity, that we filtered out testing three different models based on Gaussian process regression. As a sanity cross-check, we repeated the analyses using HARPS radial velocities extracted with three different algorithms. We used HIRES radial velocities and Hipparcos-Gaia astrometry to put constraints on the presence of long-period companions, and we analysed TESS photometric data. Results. We found strong evidence that Gl 514 hosts a super-Earth on a likely eccentric orbit, residing in the conservative habitable zone for nearly 34% of its orbital period. The planet Gl 514 b has minimum mass m b sin i b = 5.2 ± 0.9 M ⊕ , orbital period P b = 140.43 ± 0.41 days, and eccentricity e b = 0.45 +0.15 −0.14 . No evidence for transits is found in the TESS light curve. There is no evidence for a longer period companion in the radial velocities and, based on astrometry, we can rule out a ∼ 0.2 M Jup planet at a distance of ∼ 3 − 10 au, and massive giant planets/brown dwarfs out to several tens of au. We discuss the possible presence of a second low-mass companion at a shorter distance from the host than Gl 514 b. Conclusions. Gl 514 b represents an interesting science case to study the habitability of planets on eccentric orbits. We advocate for additional spectroscopic follow-up to get more accurate and precise planetary parameters. Further follow-up is also needed to investigate sub m s −1 and shorter period signals.

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