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The rate of tidal disruption events (TDEs) depends sensitively on the stellar properties of the central galactic regions. Simulations show that galaxy mergers cause gas inflows, triggering nuclear starbursts, increasing the central stellar density. Motivated by these numerical results, and by the observed overrepresentation of post-starburst galaxies among TDE hosts, we study the evolution of the TDE rate in high-resolution hydrodynamical simulations of a galaxy merger, in which we capture the evolution of the stellar density around the massive black holes (BHs). We apply analytical estimates of the loss-cone theory, using the stellar density profiles from simulations, to estimate the time evolution of the TDE rate. At the second pericentre, a nuclear starburst enhances the stellar density around the BH in the least massive galaxy, leading to an enhancement of the TDE rate around the secondary BH, although the magnitude and the duration of the increase depend on the stochasticity of star formation on very small scales. The central stellar density around the primary BH remains instead fairly constant, and so is its TDE rate. After the formation of the binary, the stellar density decreases, and so does the TDE rate. [ABSTRACT FROM AUTHOR]