Greek character well on the way to being tight (3)
I believe the answer is:
tau
'greek character' is the definition.
(letter from the Greek alphabet)
'well on the way to being tight' is the wordplay.
'well on the way to being' means to remove the last letter (the letters almost form the word).
'tight' becomes 'taut' ('taut' can be a synonym of 'tight').
'taut' with its final letter removed is 'TAU'.
(Other definitions for tau that I've seen before include "Marathon character" , "Homeric character" , "A subatomic particle" , "character from Athens" , "Letter from Greece" .)