A horse takes some feeding, by the way (5)
I believe the answer is:
steed
'a horse' is the definition.
(steed is a kind of horse)
'takes some feeding by the way' is the wordplay.
'some' says to take the initial letters.
'feeding' is an insertion indicator.
'by the way' becomes 'seed' (I am not sure about this - if you are sure you should believe this answer much more).
The initial letter of 'takes' is 't'.
't' put within 'seed' is 'STEED'.
Can you help me to learn more?
(Other definitions for steed that I've seen before include "ride" , "Literary term for horse" , "Trusty horse" , "Stallion" , "Horse, mount" .)