Not being an expert, from the technical point of view I see two issues for that:
First, breaking through Arctic ice should be a problem of buoyancy and reinforced hull. Probably not a big tech. problem for oceanic submarines of about 4,000 tonnes and above.
Secondly, patrolling the Arctic for nuclear boats is easy as they have virtually unlimited fuel which translates into high speeds when needed and no worries about endurance (just supplies).
Designing an AIP submarine to patrol the Arctic requires a naval authority (RCN/DND) to set up the criteria on the endurance, range and speed of the patrol.
Grossly speaking, take for instance a 40 days submerged patrol to cover up to 6,000 nm (including 1,500 nm, 25%, as reserve) at about 7 knots. This would require an AIP about double the power of existing ones (600-700 kW vs 250-350kW) AND a fuel reserve about 4-6 times the reserves of typical AIP boats (*). Fuel reserves mean both Hydrogen in different forms (for fuel cells) and Oxygen (liquid, LOX), or fuel (Stirling engine) and Oxygen too.
Batteries would allow for sudden sprints at higher speeds but just for few hours.
The main problem is that up to now no allied submarines have had such requirements, that leads to the RCN needing a customized design.
There was an article about this in the 2020-fall Canadian Naval Review.
(*) At least, 4 times: double the power and double the endurance, from three weeks claimed by Type 212 or swedish Gotland (just gross figures as I remember) to six weeks.