'Prince of Tyre', almost priceless bust (8)
I believe the answer is:
Here is my best explanation:
''prince of tyre'' is the definition.
'almost priceless bust' is the subsidiary indication.
'almost' means to remove the last letter.
'bust' indicates anagramming the letters.
'priceless' with its final letter taken off is 'priceles'.
'priceles' with letters rearranged gives 'pericles'.
(Other definitions for pericles that I've seen before include "Ancient Athenian leader - prince of Tyre", "Shakespearean play", "Athenian leader - Prince of Tyre", "Athenian 'golden age' leader", "Shakespeare play '......., Prince of Tyre'", "Athenian statesman", "Play by Shakespeare" and "Play - Prince of Tyre".)