Fibre from tree Greek character's going up (5)
I believe the answer is:
oakum
'fibre' is the definition.
(oakum is a kind of fibre)
'tree greek character's going up' is the wordplay.
'tree' becomes 'oak' (oak is a kind of tree).
'greek character' becomes 'mu' (letter from the Greek alphabet).
'going up' says the letters should be written backwards.
'mu' back-to-front is 'um'.
'oak'+'um'='OAKUM'
'from' is the link.
(Other definitions for oakum that I've seen before include "Tarred ropes teased out for caulking ships" , "Fibre from unravelled old rope" , "What convicts used to pick" , "Rope fibre for caulking wooden ships" , "ropy bits" .)