Started to lose heart and pulse (4)
I believe the answer is:
bean
'pulse' is the definition.
(beans are a type of pulse)
'started to lose heart' is the wordplay.
'started' becomes 'began' ('begin' can be a synonym of 'start').
'to lose heart' says to hollow out the word (remove centre letters) (I've seen 'losing heart' mean this).
'began' with its centre removed is 'BEAN'.
'and' acts as a link.
(Other definitions for bean that I've seen before include "Edible legume" , "Fava, kidney or mung, say" , "Seed of coffee plant" , "Haricot seed" , "Haricot, for example" .)