Nitrogen-bearing molecules (such as N$_ $H$^ $ and NH$_ $) are excellent tracers of high-density and low-temperature regions, such as dense cloud cores. Notably, they could help advance the understanding of snow lines in protoplanetary discs and the chemical evolution of comets. However, much remains unknown about the chemistry of N-bearing molecules on grain surfaces, which could play an important role in their formation and evolution. In this work, we experimentally study the behaviour of NH$_ $ on surfaces that mimic grain surfaces under interstellar conditions in the presence of some other major components of interstellar ices (i.e. H$_2$O, CO$_2$, CO). We measure the binding energy distributions of NH$_ $ from different H$_ $O ice substrates and also investigate how it could affect the NH$_ $ snow line in protoplanetary discs. We performed laboratory experiments using the ultra-high vacuum (UHV) set-up VENUS (VErs des NoUvelles Syntheses). We co-deposited NH$_ $ along with other adsorbates (H$_ $O, 13CO, and CO$_ $) and performed temperature programmed desorption (TPD) and temperature programmed-during exposure desorption (TP-DED) experiments. The experiments were monitored using a quadrupole mass spectrometer (QMS) and a Fourier transform reflection absorption infrared spectrometer (FT-RAIRS). We obtained the binding energy distribution of NH$_ $ on crystalline ice (CI) and compact amorphous solid water ice (c-ASW) by analysing the TPD profiles of NH$_ $ obtained after depositions on these substrates. In the co-deposition experiments, we observed a significant delay in the desorption and a decrease of the desorption rate of NH$_ $ when H$_ $O is introduced into the co-deposited mixture of NH$_ $-13CO or NH$_ $-CO$_ $, which is not the case in the absence of H$_ $O. Secondly, we noticed that H$_ $O traps roughly 5-9$<!PCT!>$ of the co-deposited NH$_ $, which is released during the phase change of water from amorphous to crystalline. Thirdly, we obtained a distribution of binding energy values of NH$_ $ on both ice substrates instead of an individual value, as assumed in previous works. For CI, we obtained an energy distribution between 3780K and 4080K, and in the case of amorphous ice, the binding energy values were distributed between 3630K and 5280K; in both cases we used a pre-exponential factor of A = 1.94times 1015s$^ From our experiments, we conclude that the behaviour of NH$_ $ is significantly influenced by the presence of water, owing to the formation of hydrogen bonds with water, in line with quantum calculations. This interaction, in turn, preserves NH$_ $ on the grain surfaces longer and up to higher temperatures, making it available closer to the central protostar in protoplanetary discs than previously thought. It explains well why the NH$_ $ freeze-out in pre-stellar cores is efficient. When present along with H$_ $O, CO$_2$ also appears to impact the behaviour of NH$_ $, retaining it at temperatures similar to those of water. This may impact the overall composition of comets, particularly the desorption of molecules from their surface as they approach the Sun.