A painted exterior door can be covered with a sealer that is compatible with the type of paint that is already painted on the door. This is not a common or a recommended practice, however. It is usually better to repaint the door. A good quality exterior paint acts as a sealer against the elements.
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The best sealer to use for giving extra protection to a painted door is either an oil-based or a water-based polyurethane sealer. For best results, use an oil-based sealer on oil paint and the same for latex. It is also possible to cover a latex paint with oil-based polyurethane. Never, however, try a water-based polyurethane on top of the oil paint. For best results, wash old paint before you apply a sealer. If the paint is new, let the paint cure for an extra few days beyond what the manufacturer recommends. Still, you should always consider repainting the door as a viable alternative to using a sealer.
Repaint the Door
Your best solution may be to re-paint the door. This is especially true if the old paint has been on the door awhile and is starting to weather. You will already have to do some prep work just to apply the clear sealer so you might as well repaint the door instead. Also, the recently developed acrylic latex paints are of such good overall quality that once the paint is applied, the weather-resistant attributes of the paint should prevent the need of an extra sealer.
Use an Acrylic Sealer
Some acrylic sealers on the market specially designed for covering unpainted masonry. Included in the manufacturer's specifications is the mention that this type of sealer may also be used on the surface of a painted exterior door to add extra protection for the door. This is not a common practice, however. You will have to prep the door in several ways before this type of acrylic sealer can be applied.
The painted door must be currently painted with a durable coat of exterior latex paint. That coat of paint needs to be cured thoroughly. Do not ever put acrylic sealer on top of oil paint. Also, the paint on the door with have to be de-glossed. It is highly unlikely that an exterior door would be painted with a flat exterior paint, but if that is the case, you do not have to de-gloss the paint. If a flat exterior paint has been used, just give the door a light washing with warm water and a tiny bit of soap. Finally, always give the door a light washing or even just a rinse before you begin. This will help with the adhesion. Benjamin Moore does make a clear acrylic sealer which, according to its specs, can be used on top of a non-gloss latex paint.