The most common and most likely answer to this crossword clue is the 3 plus 7 letter word NEW ORLEANS
I've seen this crossword clue in Independent
N
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W
O
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A
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More clues leading to the result NEW ORLEANS
- What makes Salerno a famous city
- City bank blocks corrupt owners
- Salerno may be the home of jazz
- Capital of Louisiana in answer, one gathered? This isn’t!
- Relatives welcoming role we developed for US city
- Nuclear engineer swore about list in US city
- Salerno possibly somewhere in the USA?
- By implication, learns nothing in US city?
- A port that could be Salerno
- Southern city is inclined to go after wayward owner
Buddy explains!

The straight part
We know that "home of jazz" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case home of jazz = new orleans.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.