Get tight, making Greek character catch up (6)
I believe the answer is:
tauten
'get tight' is the definition.
(I've seen this in another clue)
'greek character catch up' is the wordplay.
'greek character' becomes 'tau' (Greek letter).
'catch up' becomes 'ten' (I've seen this in other clues).
'tau'+'ten'='TAUTEN'
'making' is the link.
(Other definitions for tauten that I've seen before include "Stretch tight" , "Tense; stretch" .)