Precious rival ignores first pair at university, who are perfectly competent (8)
I believe the answer is:
valuable
'precious' is the definition.
(similar in meaning)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for valuable that I've seen before include "Expensive, prized" , "Of considerable worth" , "Of great importance or worth" , "Precious" , "Blue lava may be worth money" .)