With a better argument, American Mancini ultimately pens 'keep Moon River' (1,8)
I believe the answer is:
a fortiori
'with a better argument' is the definition.
(term for a type of argument)
'american mancini ultimately pens keep moon river' is the wordplay.
I cannot quite understand how this works, but
'american' could be 'a' (common abbreviation - e.g. in organisation names) and 'a' is located in the answer.
'keep' could be 'fort' (I've seen this in other clues) and 'fort' is found within the answer.
'moon' could be 'io' (moon of Jupiter) and 'io' is located in the answer.
'river' could be 'r' and 'r' is located in the answer.
A single letter 'i' remains which might be clued in a way I don't understand.
This may be the basis of clue (or it may be nonsense).
(Other definitions for a fortiori that I've seen before include "with better grounds" , "By inference, even more" , "For stronger reasons" , "even more convincing reasons" , "more conclusively" .)