The most common and most likely answer to this crossword clue is the 5 letter word NUMEN
I've seen this crossword clue in Financial Times
N
U
M
E
N
Buddy explains!

The straight part
We know that "spirit of Rome" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case spirit of rome = numen.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.
What does NUMEN mean?
NUMEN noun- A divinity, especially a local or presiding god.
- An influence or phenomenon at once mystical and transcendant.