A search for a right-handed gauge boson $WR$, decaying into a boosted right-handed heavy neutrino $NR$, in the framework of Left-Right Symmetric Models is presented. It is based on data from proton-proton collisions with a centre-of-mass energy of 13 TeV collected by the ATLAS detector at the Large Hadron Collider during the years 2015, 2016 and 2017, corresponding to an integrated luminosity of 80 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. The search is performed separately for electrons and muons in the final state. A distinguishing feature of the search is the use of large-radius jets containing electrons. Selections based on the signal topology result in smaller background compared with to expected signal. No significant deviation from the Standard Model prediction is observed and lower limits are set in the $WR$ and $NR$ mass plane. Mass values of the $WR$ smaller than 3.8-5 TeV are excluded for $NR$ in the mass range 0.1-1.8 TeV.