  The recent computation on the full threshold contributions to Higgs boson
production at next-to-next-to-next-to-leading order (N$^3$LO) in QCD contains
valuable information on the soft gluons resulting from virtual and real
emission partonic subprocesses. We use those from the real emissions to obtain
the corresponding soft gluon contributions to Drell-Yan production and
determine the missing $\delta(1-z)$ part of the N$^3$LO. The numerical impact
of threshold effects demonstrates the importance of our results in the
precision study with the Drell-Yan process at the LHC.
