One endlessly cherished conception (4)
I believe the answer is:
idea
'conception' is the definition.
(I've seen this in another clue)
'one endlessly cherished' is the wordplay.
'one' becomes 'i' (Roman numeral).
'endlessly' means to remove the last letter.
'cherished' becomes 'dear' (dear can mean cherished or adored).
'dear' with its last letter taken off is 'dea'.
'i'+'dea'='IDEA'
(Other definitions for idea that I've seen before include "Plato's Form is" , "Content of cognition" , "Flash of inspiration?" , "Creative spark" , "Suggestion" .)