The tiles are available online for free as long as the following attribution is used:
Map © ArcticConnect, Data © OpenStreetMap Contributors
Tiles are PNG images that are compatible with web "slippy-map" libraries. They are served using the standard XYZ url scheme:
http://airport.gswlab.ca/awm/{zoom}/{x}/{y}.png
Note that the map is in EPSG:3573 projection, so the XYZ scheme will not map to latitude/longitude the same way as regular web maps.
Here are some examples hosted on glitch.com for OpenLayers v4, v5, and v6.
Note that the API for v5 and v6 appear to be identical. Only minor changes with usage of Proj4 are required for the v4 to v5 transition.
PolarMap.js can be modified to use tiles from this new server instead of the original Arctic Connect tiles server. Please see the example for PolarMap.js where the Tile Layer is redefined in the code.
An example for Leaflet 1.0 or newer is not yet available.
If you are a user of ArcGIS Online, you can add Arctic Web Map as a base layer for your maps. Note that due to the projection, the map may not line up with other layers that are in a different spatial reference system.
In your New Map, select "Add", then "Add Layer from Web". Select "A Tile Layer" for the type of data.
URL: http://airport.gswlab.ca/awm/{level}/{col}/{row}.png
Title: Arctic Web Map
Credits: Map © ArcticConnect, Data © OpenStreetMap Contributors
Once added, you may have to drag the map "down" to see the new layer.