We present the first result of a programme to search for large flux variations in the X-ray sources of the XMM Serendipitous Survey compared to previous ROSAT observations. An increase in X-ray flux by a factor >10 was discovered from the nucleus of the galaxy NGC 7589 on a time-scale of less than 5 yr. The 0.4-10 keV XMM spectrum can be approximated by a power law with photon index of 1.7-1.8, though it seems to flatten above 5 keV, suggesting a possible complex model, such as partial covering or disc reflection. A classification based on an analysis of its optical spectrum places NGC 7589 in the Seyfert region, but close to the Seyfert-LINER (low-ionization nuclear emission-line region) borderline on the active galactic nucleus (AGN) diagnostic diagrams. We classify NGC 7589 as either Seyfert 1.9 or LINER I, in the light of the detection of a broad Ha line, which makes NGC 7589 an AGN in the low-luminosity regime. We interpret the observed variability in terms of either changes in covering factor of absorbing gas in the AGN, or variability in the intrinsic X-ray luminosity. Should the latter be the case, the inferred Eddington accretion rate increased from the radiatively inefficient accretion-dominated regime to a value close to the putative critical value, at which a transition of the accretion mode is supposed to take place. This possibility presents a new prospect of studying accretion physics in the central black holes of external galaxies by direct observing changes of 'spectral state', as is common in stellar black hole binary systems.