Sure, in the air can mean to hover – if you're talking about a helicopter, a hummingbird, or a biplane.
But consider this more metaphorical usage, listed in NOAD: in the air – noticeable all around; becoming prevalent : I smell violence in the air .
I suppose you could use hover, if you wanted to, but it wouldn't be used to replace in the air .
Instead, you might say: A sense of mystery hovered in the air.
I think that's an improvement over the original, simply because hovered is a more interesting verb than was .
There are plenty of other ways to say it, though, too.
Besides Fumble's hung in the air suggestion, there's also:
A sense of mystery clouded the air.
A sense of mystery darkened the air.
Because these are transitive verbs (and not intransitive, like hovered ), we eliminate the preposition in .
ell.stackexchange.com/users/113/J.R.
Hover and be in the air are only distantly synonymous, and only within a narrow range of reference.
Hover means to remain stationary over a particular place
Police helicopters hovered above the square.
OR to maintain a position over a particular moving object Her mother hovered over her like a suspicious vulture.
It often implies that the subject is poised to drop or pounce on the place or object.
Be in the air means to be present or sensible wherever one goes .
It usually implies that the subject is sensible to and has an effect on everyone; often it means specifically that the subject is a universal topic of discussion.
Spring is in the air.
Rumours of war were in the air.
In your case: ✲ It hovered a sense of mystery is unidiomatic.
A sense of mystery hovered adds senses of threat and locational specificity which are not present in the original, and removes, or at least attenuates, the sense of great extension and effect.
You can use hover ; but it won't mean the same thing.
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It's definitely not appropriate to rephrase using hovers .
Unless you're a highly creative writer, but that has no relevance here on ELL.
A credible alternative to the verb to be when referencing a sense of mystery might be...
A sense of mystery hung in the air
I'm not sure it makes sense to try and explain why a sense of mystery wouldn't normally "hover".
They're all metaphorical references anyway; some are used quite often, others rarely or never.
Who can say why a sense of mystery is far more likely to pervade rather than permeate ?
(it never penetrates or saturates ).
ell.stackexchange.com/users/126/FumbleFingers Reinstate Monica
"In the air" here is an idiom.
The "sense of mystery" is not literally a physical object that is floating above the floor.
In general, you cannot substitute words that by a dictionary definition are synonymous for an idiom.
That makes it no longer an idiom, so people think you mean the words literally.
There are many jokes about someone trying to learn the language who tries to substitute such synonyms and leaves native speakers confused about what he means.
That's just not how the language works.
As I write this, I'm thinking of all sorts of idioms that would lose all meaning if reworded.
Like: "I don't know the answer off the top of my head.
" I don't have that information readily available.
But, "I don't know the answer falling from my hair.
"
Not a clue what that means.
"Sally is a dog.
" Sally is ugly. "Sally is a canine.
"
She is literally the four-legged animal.
"Differential equations are over my head.
"
The subject is too difficult for me to understand.
"Differential equations are upstairs.
" The class meets on the second floor.
"We're going to go to the ball game and have a blast!
" We will have a good time.
"We're going to go to the ball game and create an explosion!
" We are planning a terrorist attack at a public event.
Etc.
One could play this game forever.
ell.stackexchange.com/users/803/Jay
float ?
There was a sense of mystery floating in the air.
or use "around" instead of " in the air" There was a sense of mystery floating around.
ell.stackexchange.com/users/1795/Derfder
There was a sense of mystery in the air.   Since "to be in the air", at least according to the dictionary I use ("i Garzantini"), can be translated using the verb "to hover", in order to make the above sentence, as to say, "more erudite", is it appropriate to rephrase it this way "It hovered a sense of mystery"? Or, maybe, "to hover" cannot be used in reference to abstract concepts?
Rephrasing "to be in the air"
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<word-choice>
ell.stackexchange.com/questions/8140
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"Hover" is not appropriate in this context. "In the air" here is an idiom. Use "around" instead of " in the air", as in:   "There was a sense of mystery floating around".   Hover is unidiomatic, in the air is idiomatic.
In the air is an idiom. Hover is unidiomatic.