Young person carrying Greek letter for mythical monster (8)
I believe the answer is:
minotaur
'for mythical monster' is the definition.
(Minotaur is an example)
'young person carrying greek letter' is the wordplay.
'young person' becomes 'minor' (I've seen this before).
'carrying' indicates putting letters inside.
'greek letter' becomes 'tau' (letter from the Greek alphabet).
'minor' enclosing 'tau' is 'MINOTAUR'.
(Other definitions for minotaur that I've seen before include "Mythical beast of Crete" , "Creature, half-man and half-bull, slain by Theseus in the Cretan maze" , "Mythical bull-headed monster" , "50 per cent ruminant" , "Monster in a maze with the head of a bull and the body of a man" .)