Search vigorously over time for plant part (7)
I believe the answer is:
rootlet
'for plant part' is the definition.
(rootlet is a kind of plant part)
'search vigorously over time' is the wordplay.
'search vigorously' becomes 'rootle' (rootle can mean to root around or search).
'over' says to put letters next to each other (in a down clue, some letters go over others).
'time' becomes 't' (abbreviation).
'rootle'+'t'='ROOTLET'
(Other definitions for rootlet that I've seen before include "Little plant part" , "Small branch of a plant's "anchor"" , "Minor growth under a plant" , "underground development" , "Small rhizome" .)