Start to grow capital, having got rid of a pest (3)
I believe the answer is:
bud
'start to grow' is the definition.
(as in a plant budding)
I don't understand the rest of the clue.
(Other definitions for bud that I've seen before include "China to America?" , "Small pre-flower knob on plant" , "American beer" , "Undeveloped flower" , "Small pre-flower knob - nip it" .)