Recurrent phases of dormancy and activity occur in the supermassive black holes in active galactic nuclei. Characterizing the duty cycles of this process is crucial in understanding the impact of the energy released on the host galaxies, and their evolution. However, it is challenging to identify sources in the quiescent and restarted phases. Our goal is to identify and characterize a substantial sample of radio galaxies in a restarted phase and explore the idea of core prominence as a signature of restarted activity. We expand our prior study of identifying restarted sources from a 30deg^2^ area in the Lockman Hole to a larger 424deg^2^ region in the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) extragalactic field using a sample of core-dominated radio galaxies selected visually. We used the 144 MHz LOFAR survey images of the HETDEX field to identify galaxies with restarting jets. By assessing diverse selection criteria including radio core dominance along with low surface brightness extended emission, spectral index properties (e.g., steep or inverted spectra of a core and an ultra-steep spectrum of extended emission), and morphology, we found 69 candidate restarted radio galaxies in the HETDEX field. The restarted candidates show a diverse intrinsic morphology, spanning from FRI, FRII, core-with-halo, to asymmetric forms, feasibly proposing different progenitors. Within these 69 restarted candidates, we identified a subset of nine galaxies characterized by ultra-steep spectrum extended emission combined with high radio core prominence, representing previous and current epochs of jet activity. We interpret our findings for this small subset as support for a model in which the switch-on and switch-off mechanism happens with a relatively fast duty cycle in these sources. We found a peculiar case, J131728.61+561544.8, which appears to have altered its jet orientation, possibly due to changes in the angular momentum or spin of its supermassive black hole, interactions with surrounding material, and/or variations in the magnetic flux threading its accretion disk. The restarted candidates span a range of radio luminosities from log_10_(L_144MHz_/(W/Hz)=23.24 to log_10_(L_144MHz_/(W/Hz)=26.80, and linear sizes between 88 and 1659 kpc at 144 MHz, with 16 sources identified as giant radio galaxies with sizes exceeding 0.7Mpc. The total stellar content of restarted sources is consistent with massive elliptical galaxies, with at least 17% inhabiting cluster environments. Our findings at z<0.4 suggest that many restarting radio galaxies are not found in rich cluster environments, aligning with the environmental properties of the broader radio-galaxy population. The present study confirms the core prominence as an effective parameter for selecting candidate restarted radio sources.