Downhearted university teacher conceals especially brief depression (10)
I believe the answer is:
despondent
'downhearted' is the definition.
(thesaurus)
'university teacher conceals especially brief depression' is the wordplay.
'university teacher' becomes 'don' (I've seen this before).
'conceals' means one lot of letters goes inside another.
'especially brief' becomes 'esp' (common abbreviation; 'brief' indicates a short form).
'depression' becomes 'dent' (synonyms).
'don' placed around 'esp' is 'despon'.
'despon'+'dent'='DESPONDENT'
(Other definitions for despondent that I've seen before include "Despairing" , "In low spirits" , "Downcast" , "Sad" , "Discouraged" .)