Hamiltonian Truncation (HT) methods provide a powerful numerical approach for investigating strongly coupled QFTs. In this work, we develop HT techniques to analyse a specific Renormalization Group (RG) flow recently proposed in refs. [1, 2–3]. These studies put forward Ginzburg-Landau descriptions for the conformal minimal models M(3, 10) and M(3, 8), as well as the RG-flow connecting them. Specifically, the RG-flow is defined by deforming the M(3, 10) with the relevant primary operator ϕ$_{1,7}$ (whose indices denote its position in the Kac table), yielding M(3, 10) + ϕ$_{1,7}$. From the perspective of HT, realising such an RG-flow presents significant challenges, as the ϕ$_{1,7}$ deformation requires renormalizing the UV theory up to third order in the coupling constant of the deformation. In this study, we carry out the necessary calculations to formulate HT for this theory and numerically investigate the spectrum of M(3, 10) + ϕ$_{1,7}$ in the large coupling regime, finding strong evidence in favor of the proposed flow.