Rushed to the heart of the forest (4)
I believe the answer is:
tore
'rushed' is the definition.
(to tear around is to rush or run fast)
'to the heart of the forest' is the wordplay.
'the heart of' says to take the centre.
The centre of 'forest' is 're'.
'to'+'re'='TORE'
(Other definitions for tore that I've seen before include "Ripped by rote" , "Ran" , "'Ripped, rent (4)'" , "Rushed" , "came apart" .)