We report the emergence of a new H I 21-cm absorption at z_abs= 1.172635 in the damped Lyα absorber (DLA) towards the γ-ray blazar PKS 2355-106 (z_em~1.639) using science verification observations (June 2020) from the MeerKAT Absorption Line Survey (MALS). Since 2006, this DLA is known to show a narrow H I 21-cm absorption at z_abs= 1.173019 coinciding with a distinct metal absorption line component. We do not detect significant H I 21-cm optical depth variations from this known H I component. A high resolution optical spectrum (August 2010) shows a distinct Mg I absorption at the redshift of the new H I 21-cm absorber. However, this component is not evident in the profiles of singly ionized species. We measure the metallicity ([Zn/H] = -(0.77 ±0.11) and [Si/H]= -(0.96 ±0.11)) and depletion ([Fe/Zn] = -(0.63 ±0.16)) for the full system. Using the apparent column density profiles of Si II, Fe II and Mg I we show that the depletion and the N(Mg I)/N(Si II) column density ratio systematically vary across the velocity range. The region with high depletion tends to have slightly larger N(Mg I)/N(Si II) ratio. The two H I 21-cm absorbers belong to this velocity range. The emergence of z_abs= 1.172635 can be understood if there is a large optical depth gradient over a length scale of ~0.35 pc. However, the gas producing the z_abs= 1.173019 component must be nearly uniform over the same scale. Systematic uncertainties introduced by the absorption line variability has to be accounted for in experiments measuring the variations of fundamental constants and cosmic acceleration even when the radio emission is apparently compact as in PKS 2355-106.