Young horse born inside (4)
I believe the answer is:
baby
'young' is the definition.
(baby is a kind of young)
'horse born inside' is the wordplay.
'horse' becomes 'bay' (I've seen this before**).
'born' becomes 'b'.
'inside' means one lot of letters goes inside another.
'bay' going around 'b' is 'BABY'.
(Other definitions for baby that I've seen before include "Honey" , "Very small (version)" , "Pet project" , "Infancy" , "Mollycoddle" .)