Explanation

The sentence in question requires a phrase that effectively connects the components of the candidates' qualifications in a manner that is grammatically correct and stylistically cohesive.

Option C, "but also work experience," is the correct choice because it employs the "not only... but also" construction, which is used to emphasize that two characteristics are being presented as important criteria. The phrase starts with "not only," suggesting that having a degree is one requirement, and the addition of "but also work experience" clearly indicates that there is a second, equally important criterion.

Let's break down why the other options are not suitable:

- Option A, "but work experience," lacks the parallel structure required; it does not provide the necessary emphasis.
- Option B, "also work experience," while it does add another qualification, does not conform to the conventional phrasing of this construction.
- Option D, "but more work experience," changes the meaning entirely, implying that quantity of experience is more relevant than just having experience.

Thus, Option C is the most appropriate choice, as it maintains the correlative structure and effectively communicates that both having a degree and possessing work experience are essential for candidates.