No officials of governments or Communist Party governing bodies in modern China use 卿 as an official position, as far as I know. So it is very confusing when 国务卿 is used for the official position of a foreign country. What kind of an official is it? What is the equivalent or counterpart in China?
In empire Time, 卿 was used by the emperor to address his cabinet members (臣)in such use as 愛卿, 眾卿, 卿等. 国务卿 is the secretary of state, that equals to 国务大臣 (宰相, 丞相) in that era.
The word was no longer in use after the creation of the new China (1911). Instead, 長 has been used for the title of the cabinet members - 院長, 部長, 處長...etc.
国务卿 is the translation for Secretary of State, equivalent counterpart in China would probably be "Minister of Foreign Affairs" (外交部长) .
However, AFAIK, its level might be higher than a typical Minister of Foreign Affairs in other countries. Not familiar with the US political system so you might want a second opinion on that.