Classic character: tense, almost to the end (3)
I believe the answer is:
tau
'classic character' is the definition.
(letter of the Greek alphabet)
'tense almost to the end' is the wordplay.
'tense' becomes 'taut' (similar in meaning).
'almost to the end' means to remove the last letter (most but not all of the word).
'taut' with its last letter removed is 'TAU'.
(Other definitions for tau that I've seen before include "letter from foreigner" , "19th letter of the Greek alphabet" , "Greek character" , "A subatomic particle" , "character from Athens" .)