(covers information from several alternate timelines)
Seniority was the concept that one outranked another by reason of age or length of term.
In 2259 of the alternate reality, despite Spock's doubts, James T. Kirk believed seniority to be a non-factor in Starfleet's decision as to who to send on a five-year mission. (Star Trek Into Darkness)
In 2371, Kathryn Janeway called out Chakotay for asking B'Elanna Torres for her opinion rather than Joseph Carey, who was the senior engineering officer between the two. He felt that none of his people would ever have seniority on USS Voyager. (VOY: "Parallax")
In 2373, Tom Paris ordered a frozen, exhausted B'elanna Torres to keep going while they were in the Argala habitat. She initially refused, saying that he couldn't order around someone with of the same rank (lieutenant, in this case). He reminded her that he had seniority, but she added that it was only "by two days". (VOY: "Displaced")