A daughter, about six, is enthusiastic (4)
I believe the answer is:
avid
'enthusiastic' is the definition.
('avid' can be similar in meaning to 'enthusiastic')
'a daughter about six' is the wordplay.
'a daughter' becomes 'ad' (I've seen this in other clues).
'about' means one lot of letters goes inside another.
'six' becomes 'vi' (roman numeral).
'ad' going around 'vi' is 'AVID'.
'is' acts as a link.
(Other definitions for avid that I've seen before include "Keenly enthusiastic" , "Zealous, enthusiastic" , "Ardent about diva" , "Showing a very keen interest in something" , "Extremely enthusiastic" .)