Drift scan observations provide the broad sky coverage and instrumental stability needed to measure the Epoch of Reionization (EoR) 21-cm signal. In such observations, the telescope’s pointing centre (PC) moves continuously on the sky. The Tracking Tapered Gridded Estimator (TTGE) combines observations from different PC to estimate $P(k_{\perp}, k_{\parallel})$ the 21-cm power spectrum, centred on a tracking centre (TC) which remains fixed on the sky. The tapering further restricts the sky response to a small angular region around TC, thereby mitigating wide-field foregrounds. Here we consider $154.2\,\mathrm{MHz}$ ($z = 8.2$) Murchison Widefield Array (MWA) drift scan observations. The periodic pattern of flagged channels, present in MWA data, is known to introduce artefacts which pose a challenge for estimating $P(k_{\perp}, k_{\parallel})$. Here we have validated the TTGE using simulated MWA drift scan observations which incorporate the flagged channels same as the data. We demonstrate that the TTGE is able to recover $P(k_{\perp}, k_{\parallel})$ without any artefacts and estimate $P(k)$ within $5 \%$ accuracy over a large $k$-range. We also present preliminary results for a single PC, combining 9 nights of observation $(17 \, \mathrm{min}$ total). We find that $P(k_{\perp}, k_{\parallel})$ exhibits streaks at a fixed interval of $k_{\parallel}=0.29 \, \mathrm{Mpc}^{-1}$, which matches $\Delta \nu_\mathrm{per}=1.28 \, \mathrm{MHz}$ that is the period of the flagged channels. Since the simulations demonstrate that the TTGE is impervious to the flagged channels, the streaks seen for the actual data are possibly caused by some systematic that has the same period as the flagged channels. These streaks are more than 3–4 orders of magnitude smaller than the peak foreground power $\mid P(k_{\perp}, k_{\parallel}) \mid \approx 10^{16} \, \mathrm{mK^2}\, \mathrm{Mpc^3}$ at $k_{\parallel}=0$. The streaks are not as pronounced at larger $k_{\parallel}$, and in some cases they do not appear to extend across the entire $k_{\perp}$ range. The rectangular region $0.05 \leq k_{\perp} \leq 0.16 \, \mathrm{Mpc^{-1}}$ and $0.9 \leq k_{\parallel}\leq 4.6 \, \mathrm{Mpc^{-1}}$ is found to be relatively free of foreground contamination and artefacts, and we have used this to place the $2\unicode{x03C3}$ upper limit $\Delta^2(k) < (1.85\times10^4)^2\, \mathrm{mK^2}$ on the EoR 21-cm mean squared brightness temperature fluctuations at $k=1 \,\mathrm{Mpc}^{-1}$.