Following this example from Cartopy lets one add a custom shape to a stereographic projection. However, the lat-lon labels with gridlines are not displaying as they're probably cut off by set_boundary(). Any way to get around this?
Minimalistic example code:
import cartopy.crs as ccrs
import cartopy.feature as cfeature
import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline # for notebook
map_projection = ccrs.NorthPolarStereo(central_longitude=0, )
data_projection = ccrs.PlateCarree()
theta = np.linspace(0, 2*np.pi, 100)
center, radius = [0.5, 0.5], 0.5 # by changing radius we can zoom in/out
verts = np.vstack([np.sin(theta), np.cos(theta)]).T
circle = mpl.path.Path(verts * radius + center)
plot_extent=[-179.9,180, 30, 90]
fig, ax1 = plt.subplots(1,1, figsize=(6,6), dpi=100, subplot_kw=dict(projection=map_projection))
ax1.set_boundary(circle, transform=ax1.transAxes)
ax1.coastlines(linewidths=1.0, color='grey')
ax1.add_feature(cfeature.BORDERS, linestyles='--', color='dimgrey', linewidths=0.8 )
ax1.set_extent(plot_extent, crs=ccrs.PlateCarree(),)
gl = ax1.gridlines(crs=ccrs.PlateCarree(), draw_labels=True,
linewidth=1, color='gray', alpha=0.5, linestyle='--', zorder=10)