sst_contour = ax.contourf(lons, lats, sst, 60, transform=ccrs.PlateCarree())

def resize_colobar(event):
    plt.draw()
posn = ax.get_position()
cbar_ax.set_position([posn.x0 + posn.width + 0.01, posn.y0, 0.04, posn.height])
fig.canvas.mpl_connect('resize_event', resize_colobar)
ax.coastlines()
plt.colorbar(sst_contour, cax=cbar_ax)
ax.gridlines()
ax.set_extent([-20, 60, 33, 63])
plt.show()
Correct placement of colorbar relative to geo axes (cartopy)