Unwanted plant; tiny and initially drooping (4)
I believe the answer is:
weed
'unwanted plant' is the definition.
(I've seen this before)
'tiny and initially drooping' is the wordplay.
'tiny' becomes 'wee' (I've seen this before).
'and' says to put letters next to each other.
'initially' indicates taking the first letters.
The first letter of 'drooping' is 'd'.
'wee'+'d'='WEED'
(Other definitions for weed that I've seen before include "Wild unwanted plant - tobacco?" , "gardening" , "Plant growing in the wrong place!" , "dope" , "Useless plant - useless person" .)