The TeV-detected nearby (z = 0.034) blazar Markarian 501 is prominent by the extreme X-ray and TeV-band variability on the diverse timescales ranging from years down to a few minutes. Since 2021 March, we observe a significantly enhanced X-ray activity of the source compared to the previous years (and comparable to the exceptional flaring behaviour shown during 2014–2015). Apparently, the source undergo variations in the baseline X-ray level on timescales of several years, which should be related to the enhanced jet collimation rate in some epochs triggered by some longterm instable processes in the accretion disc at the central supermassive black hole. A general high 0.3–10 keV level is accompanied by short-term flaring activity on timescales of 2-3 weeks, possibly triggered by the instable processes occurring in the relativistic jet closely aligned to our line-of-sight. During those instances, the X-ray spectra frequently are very hard with the photon index at 1 keV $a$<1.80, the position of the synchrotron SED peak sometimes located beyond 10 keV and the unabsorbed 0.3–10 keV flux higher than 2$\times$10^{-10} erg/cm^2/s. In such a situation, we are able to trigger the INTEGRAL Target of Opportunity observations (TOOs) simultaneously with the densely-sampled Swift campaign. Such joint effort yielded the INTEGRAL detections of Markarian 501 with (3–5)$\sigma$ significances and extension of the synchrotron SED towards the highest X-ray frequencies. These results make us capable to model the observed SED with higher accuracy and extract more information about the physical conditions in the blazar emission zone.