We consider interior static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field A α β γ , which generates, via the field strength and a potential term, a new component in the total energy-momentum tensor of the gravitational system. We formulate the field equations in Schwarzschild coordinates and investigate their solutions numerically for different equations of state of neutron and quark matter, by assuming that the three-field potential is either a constant or possesses a Higgs-like form. Moreover, stellar models, described by the stiff-fluid, radiation-like, bag model and the Bose–Einstein condensate equations of state are explicitly obtained in both general relativity and three-form gravity, thus allowing an in-depth comparison between the astrophysical predictions of these two gravitational theories. As a general result we find that, for all the considered equations of state, three-form field stars are more massive than their general relativistic counterparts. As a possible astrophysical application, we suggest that the 2.5 M ⊙ mass compact object, associated with the GW190814 gravitational wave event, could be in fact a neutron or a quark star described by the three-form gravity theory. [ABSTRACT FROM AUTHOR]