Clean out any debris or bits of old brick from the hole with a wire brush.
Patch up the interior side of the hole. How this is done will depend on the interior surface. For plaster or drywall, a small plug the size of the hole can be cut out with a drywall knife and then glued into place. Smooth drywall plaster over the hole to seal.
Mix together a batch of plastering glue to water in a thin mixture, about 1 part of glue to 5 parts water. Apply with a brush to the inside of the hole. You can also use waterproof sealant manufactured for outdoor use. Allow the hole to dry.
Mix up a batch of patching mortar for the exterior. Follow the manufacturer's instructions when mixing. If you want to match the surrounding brickwork, pulverize a piece of leftover brick that matches the rest of the wall. Mix up these pieces with the mortar.
Apply the patching mortar to the hole with a trowel. Push the mortar into the hole as you work so that it penetrates all the way to the back of the hole. Scrape off any excess.
Allow the mortar time to dry. You may need to cover the area with a plastic sheet or wet it periodically in order for it to cure fully. This will depend on the mixture used.