We evaluate the rotational velocity of stars observed by the Pristine survey towards the Galactic anticenter, spanning a wide range of metallicities from the extremely metal-poor regime ($mathrm{[Fe/H]}<-3$ dex) to nearly solar metallicity. In the Galactic anticenter direction, the rotational velocity ($V_{phi}$) is similar to the tangential velocity in the galactic longitude direction ($V_{ell}$). This allows us to estimate $V_{phi}$ from Gaia early data-release 3 (Gaia EDR3) proper motions for stars without radial velocity measurements. This substantially increases the sample of stars in the outer disc with estimated rotational velocities. Our stellar sample towards the anticenter is dominated by a kinematical thin disc with a mean rotation of $sim -220$ kms. However, our analysis reveals the presence of more stellar substructures. The most intriguing is a well populated extension of the kinematical thin disc down to $mathrm{[Fe/H]} sim -2$ dex, with a scarser extension reaching the extremely metal-poor regime, down to $mathrm{[Fe/H]} sim -3.5$ dex. In addition, a more slowly rotating kinematical thick disc component is also required to explain the observed $V_{ell}$ distribution at $mathrm{[Fe/H]} > -1.5$ dex. Furthermore, we detect signatures of a heated disc, the so-called $Splash$, at metallicities higher than $sim-1.5$ dex. Finally, at $mathrm{[Fe/H]} < -1.5$ dex our anticenter sample is dominated by a kinematical halo with a net prograde motion.
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