University angered cooks lacking the required seniority (8)
I believe the answer is:
Here is my best explanation:
'lacking the required seniority' is the definition.
'university angered cooks' is the wordplay.
'university' becomes 'u' (**).
'cooks' indicates an anagram.
'angered' with letters rearranged gives 'nderage'.
(Other definitions for underage that I've seen before include "Not legally old enough", "Not yet old enough", "Too young", "Too tender", "Immature", "one too young", "Not yet eligible to vote - too young", "Not old enough to exercise legal right" and "Need a rug (anag.)".)