There are $12$ dentists in a clinic near a school. The students of the $5$th year, who are $29$, attend the clinic. Each dentist serves at least $2$ students. Determine the greater number of students that can attend to a single dentist .
1. We start by noting that there are 12 dentists and 29 students. Each dentist serves at least 2 students. Therefore, the minimum number of students served by all dentists is:
   \[
   12 \times 2 = 24 \text{ students}
   \]
2. Since there are 29 students in total, the number of students left after each dentist serves at least 2 students is:
   \[
   29 - 24 = 5 \text{ students}
   \]
3. To maximize the number of students that a single dentist can serve, we need to assign these 5 remaining students to one of the dentists who already serves 2 students. This means that one dentist will serve:
   \[
   2 + 5 = 7 \text{ students}
   \]
4. Therefore, the greatest number of students that can attend a single dentist is 7.

The final answer is \(\boxed{7}\).