Super massive black holes at the centres of galaxies can cycle through periods of activity and quiescence. Characterising the duty cycle of active galactic nuclei (AGN) is crucial for understanding the impact of the energy they release on the host galaxy. For radio AGN, this can be done by identifying dying (remnant) and restarted radio galaxies from their radio spectral properties. Using the combination of the images at 1400 MHz produced by Apertif, the new phased-array feed receiver installed on the Westerbork Synthesis Radio Telescope, and images at 150 MHz provided by LOFAR, we have derived resolved spectral index images (at a resolution of ~15 arcsec) for all the sources within an approximately 6 deg2 area of the Lockman Hole region. In this way, we were able to select 15 extended radio sources with emission (partly or entirely) characterised by extremely steep spectral indices (steeper than 1.2). These objects represent cases of radio sources in the remnant or the restarted phases of their life cycle. Our findings confirm that these objects are not as rare as previously thought, suggesting a relatively fast cycle. They also show a variety of properties that can be relevant for modelling the evolution of radio galaxies. For example, the restarted activity can occur while the remnant structure from a previous phase of activity is still visible. This provides constraints on the duration of the “off” (dying) phase. In extended remnants with ultra-steep spectra at low frequencies, the activity likely stopped a few hundred megayears ago, and they correspond to the older tail of the age distribution of radio galaxies, in agreement with the results of simulations of radio source evolution. We find remnant radio sources with a variety of structures (from double-lobed to amorphous), possibly suggesting different types of progenitors. The present work sets the stage for exploiting the powerful tool of low-frequency spectral index studies of extended sources by taking advantage of the large areas common to the LOFAR and the Apertif surveys.