Do well with old Shakespearean duke (8)
I believe the answer is:
prospero
'shakespearean duke' is the definition.
'prospero' can be an answer for 'duke' (I've seen this before). I am unsure of the 'shakespearean' bit.
'do well with old' is the wordplay.
'do well' becomes 'prosper' (I've seen this before).
'with' is a charade indicator (letters next to each other).
'old' becomes 'o' (abbreviation).
'prosper'+'o'='PROSPERO'
Can you help me to learn more?
(Other definitions for prospero that I've seen before include "character in 20 [THE TEMPEST]" , "Usurped Duke of Milan (The Tempest)" , "Miranda's father (Tempest)" , "Role in The Tempest" , "Sorcerer of The Tempest" .)