Peris forest flame
I've a Peris with healthy new growth in places with other areas showing old barren stems with leaves at the tips. Can these barren stems be sut back to encourage new growth? When would be the best time?
Barren stems in areas.

The rest of the plant looks good

Barren stems in areas.

The rest of the plant looks good

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I would cut that dead wood back to new growth. Normally, you prune them after flowering but any deceased or damaged should be pruned out to keep the shrub healthy
Try to wash your leaves using a damp sponge. If you have any over-hanging taller shrubs, keep an eye out to see if there are issues there. It’s possibly affecting your shrub. That branch needs removing, it’s unlikely to rejuvenate.