Pruning system followed for climbing roses is

The pruning system followed for climbing roses is no pruning.
Pruning, in horticulture, is the removal or reduction of parts of a plant, tree, or vine that are not requisite to growth or production, are no longer visually pleasing, or are injurious to the health or development of the plant.
Pruning won't benefit climbing roses from being cut back hard unless there are issues with the plant and it requires renovating.