  Using the coalescence model we compute the multiplicity of $Z_{cs} (3985)^-$
(treated as a compact tetraquark) at the end of the quark gluon plasma phase in
heavy ion collisions. Then we study the time evolution of this state in the hot
hadron gas phase. We calculate the thermal cross sections for the collisions of
the $Z_{cs} (3985)^-$ with light mesons using effective Lagrangians and form
factors derived from QCD sum rules for the vertices $Z_{cs}\bar{D}_{s }^* D $
and $Z_{cs} \bar{D}_{s} D^{*}$. We solve the kinetic equation and find how the
$Z_{cs} (3985)^-$ multiplicity is affected by the considered reactions during
the expansion of the hadronic matter. A comparison with the statistical
hadronization model predictions is presented. Our results show that the
tetraquark yield increases by a factor of about $2-3$ from the hadronization to
the kinetic freeze-out. We also make predictions for the dependence of the
$Z_{cs} (3985)^-$ yield on the centrality, the center-of-mass energy and the
charged hadron multiplicity measured at midrapidity $ \left[ d N_{ch} / d \eta
(\eta < 0.5)\right]$.
