Greek character admitting a deep malaise (6)
I believe the answer is:
nausea
'malaise' is the definition.
(thesaurus)
'greek character admitting a deep' is the wordplay.
'greek character' becomes 'nu' (letter from the Greek alphabet).
'admitting' means one lot of letters goes inside another.
'deep' becomes 'sea' (I've seen this before).
'nu' enclosing 'a' is 'nau'.
'nau'+'sea'='NAUSEA'
(Other definitions for nausea that I've seen before include "Sensation of queasiness" , "Queasy feeling" , "Feeling of sickness or disgust" , "Sickness, biliousness" , "A feeling of disgust or illness" .)