Artist's base unknown in French resort virtually (7)
I believe the answer is:
cezanne
'artist's' is the definition.
(I've seen this before)
'base unknown in french resort virtually' is the wordplay.
'base' becomes 'e' (I've seen this in other clues).
'unknown' becomes 'z' (algebra).
'in' indicates putting letters inside.
'french resort' becomes 'cannes' (I've seen this before).
'virtually' means to remove the last letter (all but the last letter).
'e'+'z'='ez'
'cannes' with its final letter removed is 'canne'.
'ez' placed inside 'canne' is 'CEZANNE'.
(Other definitions for cezanne that I've seen before include "Paul --, French painter" , "Paul -, Fr. Impressionist" , "French artist" , "Paul ---, post-Impressionist" , "French post-impressionist painter" .)