  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.
