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 in another clue).
'with' says to put letters next to each other.
'heart' means to look at the middle letters.
The centre 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" .)