We present a multi-wavelength study (from X-ray to mm) of the nearby low-luminosity active galactic nucleus NGC 7213. We combine the information from the different bands to characterise the source in terms of contribution from the AGN and the host-galaxy interstellar medium. This approach allows us to provide a coherent picture of the role of the AGN and its impact, if any, on the star formation and molecular gas properties of the host galaxy. We focused our study on archival ALMA Cycle 1 observations, where the CO(2–1) emission line has been used as a tracer of the molecular gas. Using the ^3DBAROLO code on ALMA data, we performed the modelling of the molecular gas kinematics traced by the CO(2–1) emission, finding a rotationally dominated pattern. The molecular gas mass of the host galaxy was estimated from the integrated CO(2–1) emission line obtained with APEX data, assuming an α_CO conversion factor. Had we used the ALMA data, we would have underestimated the gas masses by a factor ∼3, given the filtering out of the large-scale emission in interferometric observations. We also performed a complete X-ray spectral analysis on archival observations, revealing a relatively faint and unobscured AGN. The AGN proved to be too faint to significantly affect the properties of the host galaxy, such as star formation activity and molecular gas kinematics and distribution.