It’s what’s known as a reduced relative clause. With the full clause, it would be: The Titanic was an Olympic-class passenger liner that was owned by the British shipping company White Star Line. Main clause: The Titanic was an Olympic-class passenger liner Relative clause: that was owned by the British shipping company White Star Line. Reduced relative clause: owned by the British shipping company White Star Line. Note that the “was” in the main clause and the “was” in the relative clause are two different ones, as each clause needs its own conjugated verb and its own subject (“that” in the relative clause). In a reduced clause, we eliminate the relative pronoun and we eliminate the verb “to be”. There are additional rule; you can look up the search term “reduced relative clauses”.

You already have "was" earlier in the sentence. The Titanic, an Olympic-class passenger line, was owned by the British shipping company White Star Line. = in this sentence you could say "was owned"