Final answer:
The nurse will administer PCV13 and Hib vaccines to the 3-year-old child; the rotavirus vaccine is not given beyond 8 months of age and is not needed in this case.
Step-by-step explanation:
The nurse in the clinic would anticipate administering the PCV13 (Pneumococcal Conjugate Vaccine) and the Haemophilus influenzae type B (Hib) vaccines to the 3-year-old child with asthma. The rotavirus vaccine is typically not given past 8 months of age, and therefore, this child would not receive an additional rotavirus vaccine. The PCV13 and Hib vaccines are part of the routine immunization schedule for children and are important for preventing diseases like pneumococcal infections and Hib meningitis, which the child is currently not up to date with based on the information provided.