The word "underring" is a somewhat uncommon term, with the closest synonyms being "underlying" and "implicit". Other synonyms may include "subtextual", "inherent", "latent", or "implied". These related words all connote an element of subtlety or hidden meaning, often suggesting that a deeper understanding or interpretation is required to fully comprehend the subject at hand. Whether used in a literary context or more broadly to describe underlying patterns or assumptions in a broader context, these synonyms can help to convey a sense of complexity and nuance to your writing.