The plant, a weed, will run rampant in a while (9)
I believe the answer is:
speedwell
'the plant' is the definition.
(speedwell is a kind of plant)
'a weed will run rampant in a while' is the wordplay.
I cannot really see how this works, but
an anagram of 'weed' is 'eedw' which is within the answer.
'will' could be 'll' (contracted form, as in 'he'll' - 'he will') and 'll' is found in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for speedwell that I've seen before include "Small blue flower of the genus veronica" , "Small creeping herbaceous plant with blue or pink flowers" , "Small plant, veronica" , "Flowering plant" , "bloomer?" .)