  This paper presents a new set of parameters ("tunes") for the
underlying-event model of the HERWIG 7 event generator. These parameters
control the description of multiple-parton interactions (MPI) and colour
reconnection in HERWIG 7, and are obtained from a fit to minimum-bias data
collected by the CMS experiment at $\sqrt{s} =$ 0.9, 7, and 13 TeV. The tunes
are based on the NNPDF 3.1 next-to-next-to-leading-order parton distribution
function (PDF) set for the parton shower, and either a leading-order or
next-to-next-to-leading-order PDF set for the simulation of MPI and the beam
remnants. Predictions utilizing the tunes are produced for event shape
observables in electron-positron collisions, and for minimum-bias, inclusive
jet, top quark pair, and Z and W boson events in proton-proton collisions, and
are compared with data. Each of the new tunes describes the data at a
reasonable level, and the tunes using a leading-order PDF for the simulation of
MPI provide the best description of the data.
