When it comes to describing someone who is "next in rank," there are a variety of synonyms that can be utilized. For example, this individual could be referred to as the "second-in-command," "vice-president," or "deputy." Other options might include "assistant," "associate," or "subordinate." Depending on the context, other adjectives could be added to more fully describe the person's role, such as "assistant manager" or "associate director." Ultimately, the precise term used will depend on the organization and the specific hierarchy in place, but there are numerous options available to convey the same basic idea: someone who holds a position just beneath the top-ranking individual in a given context.