We aim to characterize the nearby (23.78 pc), low-mass planetary system GJ7 (TOI-198), which consists of an M0-type star and a terrestrial planet. Using photometric data from three sectors of the Transiting Exoplanet Survey Satellite (TESS) and a follow-up on the planetary transit observed by the Characterizing ExOPlanets Satellite (CHEOPS), along with 87 precise radial velocities obtained with the Echelle SPectrograph lor Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO) spectrograph, we confidently confirm the planet and infer its properties. Planet GJ7 b has a mass of Mp = 3.17−0.65+0.64 M⊕ and a radius of Rp = 1.36 ± 0.13 R⊕. It orbits at a distance of a = 0.0675−0.0082+0.0067 au from its host star with an orbital period of P = 10.215213−0.000010+0.000011. We impose a 3σ upper limit on the planetary eccentricity of e ≤ 0.15. These parameters imply that GJ7 b has a high density, ρp = 6.89−2.78+4.27 gcm−3, positioning it within the region of the rocky, Earth-like planets on the mass─radius diagram and interior to the inner edge of the habitable zone around its parent star. Additionally, we find that the host star is a slow rotator and is slightly metal-depleted ([Fe/H] = −0.66 ± 0.10 dex), making GJ7 one of the lew planetary systems accurately characterized in the domain of subsolar iron abundances. TESS photometry does not show additional transit-like features attributable to planets with radii greater than ≍90% that of Earth. The high number of radial velocity measurements enables us to determine that possible transiting and non-transiting planet candidates with masses lower than hall the mass of GJ7 b would have eluded detection in our in-depth study. The stellar activity, although moderate, shows a significant radial velocity amplitude of about 4 ms−1 and poses a challenge lor detecting planets with masses lower than Earth around GJ7.