  A search is performed for the electroweak pair production of charginos and
associated production of a chargino and neutralino, each of which decays
through an $R$-parity-violating coupling into a lepton and a $W$, $Z$, or Higgs
boson. The trilepton invariant-mass spectrum is constructed from events with
three or more leptons, targeting chargino decays that include an electron or
muon and a leptonically decaying $Z$ boson. The analyzed dataset corresponds to
an integrated luminosity of 139 fb$^{-1}$ of proton-proton collision data
produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s}$
= 13 TeV and collected by the ATLAS experiment between 2015 and 2018. The data
are found to be consistent with predictions from the Standard Model. The
results are interpreted as limits at 95% confidence level on model-independent
cross sections for processes beyond the Standard Model. Limits are also set on
the production of charginos and neutralinos for a Minimal Supersymmetric
Standard Model with an approximate $B$-$L$ symmetry. Charginos and neutralinos
with masses between 100 GeV and 1100 GeV are excluded depending on the assumed
decay branching fractions into a lepton (electron, muon, or $\tau$-lepton) plus
a boson ($W$, $Z$, or Higgs).
