Step 1
Measure the size of the gap between the drywall and the brick.
Step 2
Use 1/4-round trim molding that's wide enough to cover the space of the gap. Cut the 1/4-round to the correct length to match the height of the wall.
Step 3
Place a tube of acrylic caulk into a caulking gun. Fill the gap with the caulk. This will be covered by the 1/4-round trim molding, but filling in the gap will prevent air flow from around the gap.
Step 4
Replace the caulk in the caulk gun with a tube of construction adhesive. Apply adhesive to the back side of the trim, and place the trim onto the drywall and brick gap.
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Step 5
Paint or stain the trim to match the color of the drywall.