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-Zeldovich (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)
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