Enthusiasm of Zoe, early regularly (4)
I believe the answer is:
zeal
'enthusiasm' is the definition.
(I know that zeal is a type of avidity)
'zoe early regularly' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'zoe'+'early'='zoeearly'
The alternate letters of 'zoeearly' are 'ZEAL'.
'of' is the link.
(Other definitions for zeal that I've seen before include "Fanaticism" , "Fervent devotion" , "Passion" , "Intense enthusiasm" , "Zest, ardour" .)