Long live Aladdin's oddly lacking composer! (7)
I believe the answer is:
'composer' is the definition.
(composer Antonio Vivaldi)
'long live aladdin's oddly lacking' is the wordplay.
'long live' becomes 'viva' (I've seen this in another clue).
'oddly lacking' means one should take alternating letters (letters in odd-numbered positions removed).
The alternating letters of 'aladdin' are 'ldi'.
(Other definitions for vivaldi that I've seen before include "Venetian composer ("The Red Priest"), d. 1741" , "Baroque Venetian composer, d.1741" , "Italian composer known as "the red priest"" , "Italian composer, Antonio (d. 1741)" , "Italian composer (the Red Priest) , d.1741" .)