Boy is without a pulse (4)
I believe the answer is:
bean
'pulse' is the definition.
(beans are a type of pulse)
'boy is without a' is the wordplay.
'boy' becomes 'ben' (boy's name).
'is without' indicates putting letters inside ('without' can be similar in meaning to 'outside').
'ben' going around 'a' is 'BEAN'.
(Other definitions for bean that I've seen before include "Haricot seed" , "Broad, French or kidney?" , "comic character" , "Haricot or runner?" , "Edible legume" .)