Cooler dude after royal's bottom cracking princess up (8)
I believe the answer is:
alcatraz
'cooler' is the definition.
Both the definition and answer are singular nouns.
Maybe you can see a link between them that I don't see?
'dude after royal's bottom cracking princess up' is the wordplay.
I cannot quite see how this works, but
'dude' could be 'cat' (American slang for man, esp in Jazz) and 'cat' is located in the answer.
'royal' could be 'r' (abbreviation) and 'r' is found in the answer.
'after' could be 'ala' ('a la' - 'in the style of ' or 'after' in French) and 'ala' is present in the leftover letters.
A single letter 'z' remains which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for alcatraz that I've seen before include "Birdman's prison" , "Island in San Francisco Bay,once a prison" , "(Former prison) island in San Francisco Bay" , "US island of a former maximum-security prison" , "Federal prison in California, 1934-63" .)