Translation:She is the third Minister of Finance in this government.
A Minister is a head of a government department. They're usually not elected. They're appointed by the head of government. The person may be a politician, but, more importantly, is supposed to have professional competence in the department they are heading. The Minister of Finance, eg, usually has a background in finance and economics. Just a sidenote regarding US agencies, the Secretaries of US agencies don't sit there and take minutes. They're the heads of the agencies.
Well, in a system where you have an unmarked form שַׂר and a form marked for femaleness, שָׂרָה, you get this kind of ambiguities. To express the four possibilites, the third strictly male one, the third male in a possible mixed line, the third strictly female one, or the third female one in a possible mixed line, you need more words to clarify the matter, if context does not make it clear. I would say הִיא שַׂר־הָאוֹצָר הַשְּׁלִישִׁי she is the third Minister of Finance to express the person count, but something like הִיא הָאִשָּׁה הַשְּׁלִישִׁית שֶׁהִיא שָׂרַת־הָאוֹצָר to express the female count. But ask experts on gender-sensitive language, if you want a more progressive viewpoint.