Terribly bad one having Blanchett resign? (8)
I believe the answer is:
abdicate
'resign?' is the definition.
(abdicating is a kind of resigning)
'terribly bad one having blanchett' is the wordplay.
'terribly' indicates anagramming the letters.
'one' becomes 'I' (Roman numeral).
'having' is a charade indicator (letters next to each other).
'blanchett' becomes 'cate' (I can't justify this - if you can you should believe this answer much more).
'bad' with letters rearranged gives 'abd'.
'abd'+'i'+'cate'='ABDICATE'
Can you help me to learn more?
(Other definitions for abdicate that I've seen before include "quit" , "Abandon" , "Give up power" , "Resign from or renounce the throne" , "step down" .)