Is there a term for a word that is only used if paired with another word?

The term you are looking for is probably fossil word:

A fossil word is a word that is broadly obsolete but remains in current use due to its presence within an idiom. Fossil status can also occur for word senses and for phrases.

Wikipedia gives the examples of “eke out” and “to and fro”.

Neither of your words is exclusively paired with a single word though. Inclement almost always collocates with weather but can also be found in “inclement conditions”. And dulcet is also found in “dulcet voice”. (Both of these examples and more can be found using the collocation feature of COCA or its sister corpora.)