Abnormal Growth on Dwarf Alberta Spruce
Don’t panic if your compact perfectly pyramidal dwarf Alberta spruce suddenly sprouts an abnormally large branch. Your plant will be fine.
The dwarf Alberta spruce (Picea glauca ‘Conica’), like many dwarf conifers, is propagated from a unique growth found growing on a "normal" plant. This mutation known as a sport and is propagated to create the unique dwarf Alberta spruce. These plants are prone to reversions where part or all of the plant reverts back to the original size and form.
In this case, the large branch has reverted back to the size of the white spruce (Picea glauca) from which the dwarf Alberta spruce was propagated.
This happens occasionally. Simply remove the larger branch flush with the branch bark collar, next to the trunk. Do this as soon as possible to prevent it from taking over and ruining the size and shape of your dwarf spruce.
A bit more information: You will see this in other cultivars of trees, shrubs, perennials and other plants. A plant with variegated foliage may produce a branch or shoot with green leaves. Just prune out the reversion to maintain the desired variegation.