The evidence for multi-messenger photon and neutrino emission from the blazar TXS 0506+056 has demonstrated the importance of realtime follow-up of neutrino events by various ground- and space-based facilities. The effort of H.E.S.S. and other experiments in coordinating observations to obtain quasi-simultaneous multiwavelength flux and spectrum measurements has been critical in measuring the chance coincidence with the high-energy neutrino event IC-170922A and constraining theoretical models. For about a decade, the H.E.S.S. transient program has included a search for gamma-ray emission associated with high-energy neutrino alerts, looking for gamma-ray activity from known sources and newly detected emitters consistent with the neutrino location. In this contribution, we present an overview of follow-up activities for realtime neutrino alerts with H.E.S.S. in 2021 and 2022. Our analysis includes both public IceCube neutrino alerts and alerts exchanged as part of a joint H.E.S.S.--IceCube program. We focus on interesting coincidences observed with gamma-ray sources, particularly highlighting the significant detection of PKS 0625-35, an AGN previously detected by H.E.S.S., and three IceCube neutrinos.