Old dairy cow longing to be raised under tree (8)

I believe the answer is:
alderney
'old dairy cow' is the definition.
The definition suggests a singular noun which matches the answer.
'longing to be raised under tree' is the wordplay.
'longing' becomes 'yen' (yen can mean a desire or longing for something).
'to be raised' shows that the letters should be reversed in order (going up in a down clue).
'under' says to put letters next to each other (below, in a down clue).
'tree' becomes 'alder' (alder tree is a kind of tree).
'yen' reversed gives 'ney'.
'ney' put after 'alder' is 'ALDERNEY'.
Can you help me to learn more?
(Other definitions for alderney that I've seen before include "Cattle" , "Third largest of the Channel Islands" , "Cow, perhaps" , "A Channel Island" , "Channel isle" .)
