Crossword Genius

Biden regularly on time visiting Conservative after no bad publicity (9)

Ross

I believe the answer is:

notoriety

'bad publicity' is the definition.
(notoriety is fame for a bad reason)

I don't understand how the remainder of the clue works.

(Other definitions for notoriety that I've seen before include "Bad publicity" , "Fame from bad deeds" , "Public exposure" , "Bad reputation" , "Infamy, disrepute" .)

I've seen this clue in The Guardian.
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