At the beginning of the mission, since our priority was to identify the origin of the alien’s signal.
what is the most accurate way to describe the excerpt?
.it is a complex sentence.
.it is an independent clause.
.it is a dependent clause.
.it is a compound sentence.

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.

It is a dependent clause.

A clause is a group of related words that have at least a subject and a verb, which may be dependent (also called subordinated) or independent. When it is dependent, the clause can not stand on its own because it does not express a complete thought, therefore it should always be part of a larger clause.

The excerpt is made up of two dependent clauses "At the beginning of the mission" and "since our priority was to identify the origin of the alien’s signal". Neither of the clauses expresses a complete thought (Something is missing!), thus, they do not make sense at all.