We present observations of the double-peaked broad Ha profile emitted by the active nucleus of NGC7213 using the Gemini South Telescope in 13 epochs between 2011 September 27 and 2013 July 23. This is the first time that the double-peaked line profile of this nucleus typical of gas emission from the outer parts of an accretion disc surrounding a supermassive black hole (SMBH) - is reported to vary. From the analysis of the line profiles we find two variability time-scales: (1) the shortest one, between 7 and 28 d, is consistent with the light travel time between the ionizing source and the part of the disc emitting the line; and (2) a longer one of greater than or similar to 3m corresponding to variations in the relative intensity of the blue and red sides of the profile, which can be identified with the dynamical time-scale of this outer part of the accretion disc. We modelled the line profiles as due to emission from a region between approximate to 300 and 3000 gravitational radii of a relativistic, Keplerian accretion disc surrounding the SMBH. Superposed on the disc emissivity, the model includes an asymmetric feature in the shape of a spiral arm with a rotation period of approximate to 21 m, which reproduces the variations in the relative intensity of the blue and red sides of the profile. Besides these variations, the rms variation profile reveals the presence of another variable component in the broad line, with smaller velocity width W68 (the width of the profile corresponding to 68 per cent of the flux) of similar to 2100 km s(-1).