Top of the bill to begin a run in variety (4,4)
I believe the answer is:
star turn
'top of the bill' is the definition.
(I've seen this before)
'begin a run in variety' is the wordplay.
'begin' becomes 'start' (synonyms).
'in variety' indicates anagramming the letters (I've seen this in other clues).
'run' with letters rearranged gives 'urn'.
'start'+'urn'='STAR-TURN'
'to' acts as a link.
(Other definitions for star turn that I've seen before include "Top act" , "Top item in entertainment" , "Most impressive act" , "Top performer" , "fine performance" .)