Yes, "his" as the subject of the second sentence isn't only implied but a logical, grammatical, and stylistically smooth use of a personal pronoun based on its clear antecedent noun in the previous sentence, which in this case is "Sec. Remulla." Writers with lesser confidence in their correlative grammar would have written that second sentence either as "Truly, Secretary Remulla's job is a most stressful, perilous, and thankless one" or "Truly, his job is a most stressful, perilous, and thankless one," perhaps even as "Truly, his job is most stressful, perilous, and thankless." However, none of these constructions exhibits the subtle, effortless, yet powerful semantic glue that binds the second sentence to the first sentence in the original construction. I must say that such writing is the mark of a good professional writer.
