Potted evergreen vine in part sun/shade, well watered. Leaves are going brown starting from the edges.
The brown edges may well just be sun scorch - variegated plants are very liable to this. Being in a pot won't help with its water regime, either.
Climbing hydrangea (Hydrangea petiolaris). Theoretically, it should be fine growing in part sun/shade with adequate watering but the hot and dry summer weather we've been having seems to be taking a toll.
Variegated form burning in too much sun exposure. If you cannot move it into a less bright position now do it as soon as possible. With cutting back not being an improvement on marginal leaf burn. It being a trading of some partial foliage damage for entire stems being lost, leaves and all.