You can use mapaxes (part of the Mapping Toolbox) to plot at the north pole.
Below is an example of how you could do this using the newmap command to create a new mapaxes with the correct projected coordinate reference system (see projcrs for more information about projected coordinate reference systems).
My colleague on the Mapping Toolbox team suggested that 3575 centers on Europe and worked well for this data set but you could also use 5041 for the North Pole region.
ev1lat = 86.369000000000000;
ev1lon = 37.531999999999996;
lat_ev1 = [83.319267272949219 83.319267272949219; 85.881607475775184 86.516294253857154];
long_ev1 = [26.007266362508137 26.007266362508137; 47.122037071396896 25.771802834435800];
lat_mean_line_ev1 = [83.319267272949219 86.347161584239785];
long_mean_line_ev1 =[26.007266362508137 37.946471827237978];
coord_lat_range_tracklines_map = '84 87';
coord_long_range_tracklines_map = '0 30';
mx = newmap(projcrs(3575));
plot(mx,ev1lat,ev1lon,"pentagram",'Color',[0.6350 0.0780 0.1840],'MarkerSize',15)
hold on
plot(mx,lat_ev1,long_ev1,'--','Color','red','LineWidth',3)
plot(mx,lat_mean_line_ev1,long_mean_line_ev1,'Color','black','LineWidth',2)
Note that mapaxes does not support base maps, but you can still plot geographic boundaries on the map if you need that for context. The documentation page for mapaxes has some examples.
