A bird lands on the fence. Your dog races outside, barking while the bird flies away. From your dog's point of view, the action may have worked. Shouting from the kitchen rarely makes the bird or the excitement disappear.
For now, supervise garden time and use a secure lead if your dog charges a fence, risks jumping it, or could reach wildlife. Check that gates and boundaries are safe. Do not leave them outside to rehearse the chase for long stretches. A sudden increase in barking or unusual agitation deserves a veterinary check.
Practice before the bird arrives
In a quiet part of the garden, reward your dog for responding to their name and coming toward you. Teach a simple "find it" game by scattering a few treats in grass away from the fence, where it is safe for them to eat. When a bird appears at a distance and your dog is still able to respond, cue the turn or game and guide them inside or to a calmer spot. Do not wait until they are sprinting at the boundary.
Look at what draws birds to the most troublesome area. You may be able to move a feeder out of sight or prevent your dog from accessing one section of the yard, without harming wildlife. Provide other outlets for sniffing and play. If the dog becomes so fixed on birds that they cannot disengage even at a distance, seek qualified, reward-based behavior help.
The goal is not to make birds uninteresting. It is to stop the fence line from becoming the daily place where your dog loses control. For more on managing attention to moving wildlife, see the dog-chasing guide, supervise garden time and keep the boundary secure
Sources: Dogs Trust: How to stop your dog chasing cars, bikes and animals. Dogs Trust: Barking - causes, triggers and how to help.