Vivien, say, supports artist, one of Elizabeth's favourites (7)
I believe the answer is:
raleigh
'one of elizabeth's favourites' is the definition.
(Sir Walter Raleigh, favourite of Elizabeth I)
'vivien say supports artist' is the wordplay.
'vivien say' becomes 'Leigh' (actress Vivien Leigh).
'supports' says to put letters next to each other (bottom letters provide a support for the top ones).
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'leigh' put after 'ra' is 'RALEIGH'.
(Other definitions for raleigh that I've seen before include "Elizabethan courtier" , "Did he fetch tobacco" , "Courtier favourite of Elizabeth I" , "SECOND PART OF 12 ACROSS" , "Tudor courtier" .)