'Prince of Tyre', almost priceless bust (8)
I believe the answer is:
pericles
'prince of tyre' is the definition.
(I've seen this before)
'almost priceless bust' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'bust' indicates an anagram.
'priceless' with its final letter removed is 'priceles'.
'priceles' anagrammed gives 'PERICLES'.
(Other definitions for pericles that I've seen before include "Ceps rile up the Athenian who ordered the construction of the Parthenon" , "Athenian statesman" , "Ancient Athenian leader - prince of Tyre" , "Athenian 'golden age' leader" , "Statesman in Athens" .)