The most accurate way to describe the excerpt is, it is a dependent clause.
The dependent clause does not express a complete meaning of a sentence. it includes a subject and a verb. These clauses include adjective clauses, adverb clauses, and noun clauses.
In the above sentence, "since our priority was to identify the origin of the alien’s signal."
It contains adverbial clause.
An adverbial clause begins with the subordinating conjunction such as if, although, because and so forth.
In it, 'since' is subordinating conjunction and 'our priority' is an adverbial clause.