Children get penny that's in the middle of pudding (4)
I believe the answer is:
seed
'children' is the definition.
(seed can mean one's offspring)
'penny that's in the middle of pudding' is the wordplay.
I cannot quite understand how this works, but
'penny' could be 'd' (pre-decimalisation abbreviation for penny) and 'd' is present in the answer.
'middle' could be 'see' (see is a kind of middle) and 'see' is found within the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'get' is the link.
Can you help me to learn more?
(Other definitions for seed that I've seen before include "One of the outstanding players in a tournament" , "Kernel" , "From which things grow" , "Biblical children" , "Top Wimbledon player" .)