Flourish, develop quickly (7)
I believe the answer is:
burgeon
I believe this is a double definition.
'flourish' is the first definition.
(I've seen this before)
'develop quickly' is the second definition.
(I've seen this before)
(Other definitions for burgeon that I've seen before include "develop quickly" , "Grow and flourish" , "bud" , "sprout" , "produce sprouts" .)