The first clause:
No Senator or Representative shall, during the time for which he was elected, be appointed to any civil office under the authority of the United States, which shall have been created, or the emoluments whereof shall have been increased during such time:
means:
If an office is created, or the salary, benefits or or other compensation of an existing office is increased during the term of an elected Senator or Representative, that sitting Senator or Representative is not eligible for appointment to that office.
The language is specific that period of interest is the "time for which he was elected" and not the "time for which he serves." Technically this prevents Senators and Representative from creating an office for themselves or lining their own pockets prior to appointments UNLESS they wait until their term of Elected Office is over.
Hilary was a sitting Senator when the Senate increased the emoluments (salary) of the office of the Secretary of State. Her term has not yet ended. According to this Constitutional restriction, she would not be eligible for appointment to that office (or any other office similarly affected) until after her Senatorial term expires.
Pesky thing, that Constitution!
Seems like “the term for which he was elected” is pretty easy to understand. You can’t just opt out by resigning.
But in the end, does it really matter? Has the US Constitution really driven much of anything of late?