We present the follow-up campaign of the luminous red nova (LRN) AT~2019zhd, the third event of this class observed in M 31. The object was followed by several sky surveys for about five months before the outburst, during which it showed a slow luminosity rise. In this phase, the absolute magnitude ranged from M_r=-2.8+-0.2 mag to M_r=-5.6+-0.1 mag. Then, over a four-five day period, AT 2019zhd experienced a major brightening, reaching at peak M_r=-9.61+-0.08 mag, and an optical luminosity of 1.4x10^39 erg/s. After a fast decline, the light curve settled onto a short-duration plateau in the red bands. Although less pronounced, this feature is reminiscent of the second red maximum observed in other LRNe. This phase was followed by a rapid linear decline in all bands. At maximum, the spectra show a blue continuum with prominent Balmer emission lines. The post-maximum spectra show a much redder continuum, resembling that of an intermediate-type star. In this phase, Halpha becomes very weak, Hbeta is no longer detectable and a forest of narrow absorption metal lines now dominate the spectrum. The latest spectra, obtained during the post-plateau decline, show a very red continuum (T_eff ~ 3000 K) with broad molecular bands of TiO, similar to those of M-type stars. The long-lasting, slow photometric rise observed before the peak resembles that of LRN V1309 Sco, which was interpreted as the signature of the common-envelope ejection. The subsequent outburst is likely due to the gas outflow following a stellar merging event. The inspection of archival HST images taken 22 years before the LRN discovery reveals a faint red source (M_F555W=0.21+-0.14 mag, with F555W-F814W = 2.96+-0.12 mag) at the position of AT 2019zhd, which is the most likely quiescent precursor. The source is consistent with expectations for a binary system including a predominant M5-type star.