Illustrious former student left to join navy base (5)
I believe the answer is:
noble
'illustrious' is the definition.
(I've seen this in another clue)
'former student left to join navy base' is the wordplay.
'former student' becomes 'OB' (abbreviation for 'Old Boy').
'left' becomes 'l' (common abbreviation).
'to join' says to put letters next to each other.
'navy' becomes 'N' (common abbreviation eg in RN Royal Navy).
'base' becomes 'e' (Euler's number - base of natural logarithms).
'ob'+'l'='obl'
'obl' put after 'n' is 'nobl'.
'nobl'+'e'='NOBLE'
(Other definitions for noble that I've seen before include "eg Earl" , "Grand, magnanimous" , "with a title?" , "Lord" , "Illustrious - of high birth - old gold coin" .)