  The complete characterization of the pressure profile of high-redshift galaxy
clusters, from their core to their outskirts, is a major issue for the study of
the formation of large-scale structures. It is essential to constrain a
potential redshift evolution of both the slope and scatter of the
mass-observable scaling relations used in cosmology studies based on cluster
statistics. In this paper, we present the first thermal Sunyaev-Zel'dovich
(tSZ) mapping of a cluster from the sample of the NIKA2 SZ large program that
aims at constraining the redshift evolution of cluster pressure profiles and
the tSZ-mass scaling relation. We have observed the galaxy cluster PSZ2
G144.83+25.11 at redshift $z=0.58$ with the NIKA2 camera, a dual-band (150 and
260 GHz) instrument operated at the IRAM 30-meter telescope. We identify a
thermal pressure excess in the south-west region of PSZ2 G144.83+25.11 and a
high redshift sub-millimeter point source that affect the intracluster medium
(ICM) morphology of the cluster. The NIKA2 data are used jointly with tSZ data
acquired by the MUSTANG, Bolocam and $Planck$ experiments in order to
non-parametrically set the best constraints on the electronic pressure
distribution from the cluster core ($\rm{R} \sim 0.02 \rm{R_{500}}$) to its
outskirts ($\rm{R} \sim 3 \rm{R_{500}} $). We investigate the impact of the
over-pressure region on the shape of the pressure profile and on the
constraints on the integrated Compton parameter $\rm{Y_{500}}$. A hydrostatic
mass analysis is also performed by combining the tSZ-constrained pressure
profile with the deprojected electronic density profile from XMM-$Newton$. This
allows us to conclude that the estimates of $\rm{Y_{500}}$ and $\rm{M_{500}}$
obtained from the analysis with and without masking the disturbed ICM region
differ by 65 and 79% respectively. (abridged)

Cosmology and Nongalactic Astrophysics