Repointing brickwork, also known as tuckpointing, is the process of removing deteriorated or damaged mortar from the joints between bricks and replacing it with fresh mortar. Here's a step-by-step process for repointing brickwork:

1. **Assess the condition**: Inspect the brickwork to identify areas where the mortar is deteriorated, cracked, or damaged. Determine the extent of the repointing needed and whether any bricks need to be replaced.

2. **Prepare the work area**: Protect the surrounding surfaces and landscaping with plastic sheeting or drop cloths to catch debris and prevent damage. Use a wire brush or chisel to remove any loose mortar or debris from the joints.

3. **Remove old mortar**: Use a pointing chisel, mortar rake, or angle grinder equipped with a mortar removal blade to carefully remove the old mortar from the joints. Take care not to damage the surrounding bricks or mortar joints.

4. **Clean the joints**: Use a stiff-bristled brush or a vacuum cleaner to clean out any remaining debris or dust from the joints. Rinse the joints with water to remove any loose particles and allow them to dry completely before proceeding.

5. **Mix fresh mortar**: Mix a batch of mortar to the desired consistency, following the manufacturer's instructions. Use a mortar mix that matches the color, composition, and strength of the existing mortar to ensure compatibility and durability.

6. **Apply mortar to joints**: Load a mortar hawk or pointing trowel with fresh mortar and press it into the cleaned joints, working from the bottom of the wall to the top. Fill the joints evenly and completely, making sure to compact the mortar and remove any air pockets.

7. **Tool the joints**: Use a pointing trowel or a jointing tool to shape and finish the mortar joints to match the surrounding brickwork. Create a uniform profile and smooth finish, taking care to match the style and appearance of the existing joints.

8. **Clean excess mortar**: Use a damp sponge or brush to clean any excess mortar from the surface of the bricks before it hardens. Be careful not to disturb the newly repointed joints or damage the surrounding bricks.

9. **Allow mortar to cure**: Allow the repointed mortar to cure for the recommended time before subjecting it to heavy loads or moisture. Keep the repointed area protected from rain, direct sunlight, and extreme temperatures during the curing process.

10. **Inspect and touch up**: Once the mortar has cured, inspect the repointed joints for any imperfections or areas that may need touch-up. Address any issues promptly to ensure a professional-quality finish.

By following these steps and taking care to properly prepare, mix, apply, and finish the mortar, you can effectively repoint brickwork and restore the appearance and structural integrity of your masonry.