Care for little flower's endless shoot (7)
I believe the answer is:
tendril
'shoot' is the definition.
(a shoot from a plant)
'care for little flower's endless' is the wordplay.
'care for' becomes 'tend' (I've seen this before).
'little flower' becomes 'rill' (a small stream - something which flows).
'endless' means to remove the last letter.
'rill' with its last letter taken away is 'ril'.
'tend'+'ril'='TENDRIL'
(Other definitions for tendril that I've seen before include "Climbing plant's supporter" , "Climbing plant's means of support" , "Climbing plant's grasper" , "Gripping part of climbing plant" , "Slender thread-like appendage of a plant" .)