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We study the formation and evolution of the tidal tail released from a young Pleiades-like star cluster, due to expulsion of primordial gas in a realistic gravitational field of the Galaxy. The tidal tails (as well as clusters) are integrated from their embedded phase for 300 Myr. We vary star formation efficiencies (SFEs) from 33% to 100% and the timescales of gas expulsion as free parameters, and provide predictions for the morphology and kinematics of the evolved tail for each of the models. The resulting tail properties are intended for comparison with anticipated Gaia observations in order to constrain the poorly understood early conditions during the gas phase and gas expulsion. The simulations are performed with the code Nbody6 including a realistic external gravitational potential of the Galaxy, and an analytical approximation for the natal gaseous potential. Assuming that the Pleiades formed with rapid gas expulsion and an SFE of $\approx 30$%, the current Pleiades are surrounded by a rich tail extending from $\approx 150$ to $\approx 350$ pc from the cluster and containing 0.7 to 2.7 times the number of stars in the present-day cluster. If the Pleiades formed with an SFE close to 100%, then the tail is shorter ($\lesssim 90$ pc) and substantially poorer, containing only $\approx 2$% of the number of present-day cluster stars. If the Pleiades formed with an SFE of $\approx 30$%, but the gas expulsion was adiabatic, the tail signatures are indistinguishable from the case of the model with 100% SFE. The model takes into account the estimated contamination due to the field stars and the Hyades-Pleiades stream, which constitutes a more limiting factor than the accuracy of the Gaia measurements.