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 subsidiary indication.
'university' becomes 'u'.
'cooks' indicates an anagram.
'angered' is an anagram of 'nderage'.
(Other definitions for underage that I've seen before include "Not yet eligible to vote - too young", "Too young", "Need a rug (anag.)", "Not old enough to exercise legal right", "Not legally old enough" and "Immature".)