  A search for a long-lived, heavy neutral lepton ($\mathcal{N}$) in 139
fb$^{-1}$ of $\sqrt{s}=13$ TeV $pp$ collision data collected by the ATLAS
detector at the Large Hadron Collider is reported. The $\mathcal{N}$ is
produced via $W \rightarrow \mathcal{N} \mu$ or $W \rightarrow \mathcal{N} e$
and decays into two charged leptons and a neutrino, forming a displaced vertex.
The $\mathcal{N}$ mass is used to discriminate between signal and background.
No signal is observed, and limits are set on the squared mixing parameters of
the $\mathcal{N}$ with the left-handed neutrino states for the $\mathcal{N}$
mass range $3$ GeV $< m_{\mathcal{N}} < 15$ GeV. For the first time, limits are
given for both single-flavor and multiflavor mixing scenarios motivated by
neutrino flavor oscillation results for both the normal and inverted
neutrino-mass hierarchies.
