Notable achievement moving a cheese (4)
I believe the answer is:
feta
'cheese' is the definition.
(type of cheese)
'notable achievement moving a' is the wordplay.
'notable achievement moving' becomes 'fet' (I can't justify this - if you can you should believe this answer much more).
'fet'+'a'='FETA'
Can you help me to learn more?
(Other definitions for feta that I've seen before include "Salty goat or sheep milk cheese" , "Greek salad cheese" , "10 down cheese" , "Greek cheese from goat or sheep milk" , "Goat's or sheep's milk cheese" .)