Hasten with beating heart, little one (4)
I believe the answer is:
runt
'little one' is the definition.
(I've seen this before)
'hasten with beating heart' is the wordplay.
'hasten' becomes 'run' (I've seen this before).
'with' says to put letters next to each other.
'heart' says to take the centre.
The middle of 'beating' is 't'.
'run'+'t'='RUNT'
(Other definitions for runt that I've seen before include "Weak individual" , "Smallest squealer" , "stunted figure" , "Small pig" , "Weak little squealer" .)