Very independent lady dancing outside with enthusiasm (6)
I believe the answer is:
avidly
'with enthusiasm' is the definition.
(I've seen this before)
'very independent lady dancing outside' is the wordplay.
'very' becomes 'v' (abbreviation).
'independent' becomes 'i'.
'dancing' indicates an anagram.
'outside' means one lot of letters goes inside another.
'lady' is an anagram of 'adly'.
'v'+'i'='vi'
'vi' inserted inside 'adly' is 'AVIDLY'.
(Other definitions for avidly that I've seen before include "In enthusiastic manner" , "With keenness" , "With eagerness" , "with enthusiasm" , "with a lot?" .)