Jefferson's First Lady with drug an inebriate performer (4,7)
I believe the answer is:
judy garland
'performer' is the definition.
(Judy Garland was a singer and actress)
'jefferson's first lady with drug an inebriate' is the wordplay.
'jefferson's first' becomes 'j' (1st letter of 'jefferson').
'with' is a charade indicator (letters next to each other).
'inebriate' indicates anagramming the letters (inebriate means drunk).
'drug'+'an'='drugan'
'lady' put after 'drugan' is 'druganlady'.
'druganlady' anagrammed gives 'udygarland'.
'j'+'udygarland'='JUDY GARLAND'
(Another definition for judy garland that I've seen is " American actress, star of "The Wizard of Oz" (1939)".)