Budding artist initially wearing new perfume (7)
'budding' is the definition.
'artist initially wearing new perfume' is the wordplay.
'initially' says to take the initial letters.
'wearing' means one lot of letters goes inside another.
'new' becomes 'n'.
'perfume' becomes 'scent' ('scent' can be a synonym of 'perfume').
The first letter of 'artist' is 'a'.
'a' inserted inside 'nscent' is 'NASCENT'.
(Other definitions for nascent that I've seen before include "Beginning to develop, embryonic", "Newly-formed", "Coming alive", "Emerging, in the process of being born", "Just setting out".)