Although not exactly a spice, fish sauce (nam pla in Thai, I think) is an excellent source of umami. In addition to monosodium glutamate, you won't find umami-rich spices. There are certain foods that are produced as a concentration (such as fish sauce) to maximize glutamates (what produces umami, umami) and others that are used as a source of umami, such as the shell of a block of Parmesan cheese in certain soups. The other option that could be used as a spice would be ground mushrooms, particularly shiitake, perhaps porcini.
Of course, this will give you a strong mushroom flavor along with the umami. Some people recommend combining them with miso for more umami and a more balanced flavor. The two things that come to mind are yeast extract (marmita, vegemita, cenovis, etc. However, I don't know if you would classify them as spices).
Many want to know if umami is a specific spice or herb. Umami is not a different spice or herb, but rather an essential flavor characteristic of some spices and herbs that contain a high concentration of glutamic acid. With a luxurious and inviting texture, this harmonious blend of winter fruits and spices is prepared as a warm cup of joy that will surely immerse you in the spirit of the season. You can experiment by combining sweet paprika, cumin, allspice, tamarind, parsley, cacao, or cinnamon with umami-rich foods.
This unique blend of mushrooms, tomatoes, onions and spices, which in Japanese means “delicious treat”, will enhance the deep, salty flavors of beef, poultry and vegetables. However, if you're looking for something that you can use in the same way as a spice, I suggest that you simply mix dried porcini mushrooms (ceps) in a blender or grinder to a fine powder and use it. Again, it's not a spice, but similar to ElendilTheTall's suggestion about powdered mushrooms would be to grind dried algae. It is more than the spice, but the food, the size of the distribution, the method and the cooking process to combine and enhance the flavor.
It's like saying what spices taste salty because I don't want to use salt; only salty spices will taste salty. Spices such as green cardamom and herbs such as bay leaves have striking and bright profiles and combine perfectly with a wide range of umami foods. These spices provide a certain earthy quality, sweetness, warmth, wood flavor, etc., which play creatively with glutamates and help create a round, full-bodied appeal in various dishes.