Depends on what the substraight is…(wood, dry wall, plaster, metal, brick, block etc)  but Not usually… if the old paint is in good condition and is free from grease, stains or spackled repairs… and is not too dark in color… you can paint it with 1 coat of High Quality Paint… otherwise spot prime stains or spackled repairs with a Pigmented Shellac Sealer Primer OR you could give a dark color just a “Wash Coat” with the finished paint, then give it a final coat with the same paint… see my site for more help in Priming… Good Luck!