Usually after its flowered, around early June, but you can remove any dead or dying growths now.

hi there ~ this info is from the RHS
Some climbers and wall shrubs respond better when cut back to a main framework of branches, rather than to near ground level. Cutting to a bud or branch helps ensure that re-growth will be successful.

Examples of plants that respond well to this method include Actinidia, Billardiera, Bougainvillea, Callistemon, Escallonia and Passiflora (passion flower).

In general, plants that flower on the previous season’s growth are pruned immediately after flowering. These plants often flower in winter, spring or early summer.

Plants that flower on the current season’s growth are often pruned in late winter or early spring. These plants usually flower in mid- to late summer, or in autumn. Some (such as Callistemon) require summer pruning after flowering.

hope this helps! Arlene