Substitute for Anchovy Paste in Recipes

Further ideas (in addition to Japanese, Parmesan and msg mentioned) for replacements for anchovies and/or paste.
Depending on the cuisine, and whether the original recipe calls for using them just added in or cooked.
Fermented paste (marmite or vegemite), small amounts of chopped cured meat, sardines or shrimp paste (if not allergic to one or both), chiles in raw, dried or pickled format, some sort of good salt if that’s the flavor note you’re looking to emphasize - sea salt, flaked salt like kosher salt, or smoked salt.

Are you allergic to anchovies or all fish?

Often anchovies/anchovy paste is included in a dish for umami, not to lend a fish flavor.

Some use Worcestershire sauce in a pinch; the Lea & Perrins original sauce has anchovies as an ingredient. Naturally Asian fish sauces provide umami.

For other sources of umami, you could use the standard Japanese sources of umami: kombu (kelp), katsuobushi (smoked bonito), or reconstituted dried shiitake mushrooms.

Depending on the dish, you could use Parmesan cheese which also has umami and might already be in your fridge. I'll leave it to you to use your favorite search engine to identify other sources of umami.

Of course, there's always the option of using synthesized MSG, developed because the extraction of naturally occurring MSG from seaweed is resource intensive.

Best of luck.