Rushed and broke spade, losing heart (4)
I believe the answer is:
sped
'rushed' is the definition.
('speed' can be a synonym of 'rush')
'broke spade losing heart' is the wordplay.
'broke' indicates anagramming the letters.
'losing heart' says to hollow out the word (remove centre letters).
'spade' with its middle removed is 'spde'.
'spde' is an anagram of 'SPED'.
'and' is the link.
(Other definitions for sped that I've seen before include "was 8 [FLEET]" , "Made haste" , "Travelled quickly" , "Went fast" , "got a move on" .)