Stubborn ex-students can eat out (9)
I believe the answer is:
obstinate
'stubborn' is the definition.
(I know that stubborn can be written as obstinate)
'ex-students can eat out' is the wordplay.
'ex-students' becomes 'OBs' (abbreviation for old boys, private school alumni).
'can' becomes 'tin' (both are metal containers).
'out' indicates an anagram (out can mean wrong or inaccurate).
'eat' is an anagram of 'ate'.
'obs'+'tin'+'ate'='OBSTINATE'
(Other definitions for obstinate that I've seen before include "Stubbornly persistent" , "headstrong" , "Female bird" , "Mulish" , "Stubborn or unyielding" .)