No, as admission to Bergen Cathedral is free, there are no tickets to purchase on site.
Since there is no entrance fee for Bergen Cathedral, visitors do not need to buy tickets, either in advance or on-site. You can simply walk in during opening hours. This directly contrasts with many other major European religious sites that might charge an admission fee.
This policy means less planning is required regarding ticketing logistics. Visitors can spontaneously decide to visit. While there might be occasional special events or concerts that could require a ticket, general sightseeing access during normal operating hours remains free of charge. Therefore, do not look for a ticket counter; directly enter the cathedral.