Regret admitting a noted figure to the show (5)
I believe the answer is:
revue
'the show' is the definition.
(revue is a kind of show)
'regret admitting a noted figure' is the wordplay.
'regret' becomes 'rue' ('rue' can be a synonym of 'regret').
'admitting' means one lot of letters goes inside another.
'a noted figure' becomes 'ev' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'rue' enclosing 'ev' is 'REVUE'.
'to' acts as a link.
Can you help me to learn more?
(Other definitions for revue that I've seen before include "Entertainment with sketches, songs etc" , "(Of butter) tasting off" , "Entertainment consisting of sketches" , "Variety show with mixed entertainments" , "Topical variety show" .)