Is a name recollected? Not with this! (7)
I believe the answer is:
amnesia
'not with this' is the definition.
The definition suggests a singular noun which matches the answer.
'is a name recollected?' is the wordplay.
'recollected?' indicates anagramming the letters (I've seen 'recollected' mean this).
'is'+'a'+'name'='isaname'
'isaname' with letters rearranged gives 'AMNESIA'.
Can you help me to learn more?
(Other definitions for amnesia that I've seen before include "As a mine (anag)" , "illness" , "Elephants won't suffer such" , "Asia men with memory loss (7)" , "Memory-loss" .)