In many cases, the air will remove itself. Remember, the best cure for this problem is prevention. These cartridges are most commonly made by Hewlett-Packard. Refilling these cartridges always involves putting an air-tight seal somewhere in the process. Depending upon the cartridge, we may seal with a set screw, or we will suggest some plastic material be used, such as hot wax, hot glue, or silicone rubber.
Hot glue is our favorite, since it seals quickly.
The vacuum will stabilize by leaking a few drops of ink. Expect this and plan for it. But a regular dribble means that you didn't get the seal tight. Because the original ink can foam in the presence of air, the first refill will often result in missing segments from long horizontal lines. This is caused by the foam blocking off the ink flow for short periods of time.