Star shown up in solo discography (4)
I believe the answer is:
idol
'star' is the definition.
(I know that idol is a type of star)
'up in solo discography' is the wordplay.
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'in' says the answer is hidden in the clue.
'lodi' is hidden within 'solo discography'.
'lodi' reversed gives 'IDOL'.
'shown' is the link.
(Other definitions for idol that I've seen before include "Honoured figure" , "Object of worship (or love?)" , "Sacred image" , "As before, fake" , "Favourite" .)