This note presents a search for a new resonance $W^\prime$ decaying into a $W$ boson and a 125~\mathrm{GeV} Higgs boson $H$ in the $\ell\nu bb$ final state, where $\ell = e,$ or $\mu$, using $pp$ collision data at 13 TeV corresponding to an integrated luminosity of 139 fb$^{-1}$ collected by the ATLAS detector at the LHC. The search is conducted by examining the reconstructed invariant mass distributions of $W^\prime \to WH$ candidates in the mass range from $400$ $\mathrm{GeV}$ to $5$ $\mathrm{TeV}$. No significant excess is observed and $95$ % confidence level upper limits between 1.3 pb and 0.56 fb are placed on the production cross-section times branching fraction of $W'$ bosons in Heavy-Vector-Triplet models.

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