The most luminous quasars are often created by major, gas-rich mergers and E1821+643, an optically luminous quasar situated at the center of a cool-core cluster, appears to be in the late stages of the post-merger blowout phase. This quasar has also been identified as a gravitational recoil candidate in which the supermassive black hole (SMBH) has received a recoil kick due to anisotropic emission of gravitational waves during the coalescence of a progenitor SMBH binary. Hubble Space Telescope images show that the quasar nucleus is spatially offset relative to surrounding [OIII]λλ4959,5007 emission, consistent with a recoil displacement, but this could also be explained by a polar wind emanating from the nucleus. We analyze long-slit spectra of the extended, ionized gas surrounding E1821+643, to study its kinematics and ionization. We have identified three kinematically distinct components, which we associate, respectively, with a wide-angle polar wind from the nucleus, an undisturbed ambient gas photoionized by the quasar and third, a redshifted stream of gas, at a distance of 3-4″ (13-18 kpc) from the nucleus, which is also photoionized by the quasar. The latter component coincides with the northern and eastern extremities of an arc of [OIII] emission seen in the HST images. This feature could indicate tidal tails originating from a merger with a gas-rich galaxy to the South-East of the nucleus, whose presence has been inferred by Aravena et al. from the detection of CO emission.