Most definitely in a much older style. Very 60’s pop rock.
There’s The Darkness, who do the whole 70s/80s glam metal thing.
This song would be perfectly at home in the 60s.
Caroline Polachek said that, when making “So Hot You’re Hurting My Feelings”, it was impossible to use her Juno-60 synth keyboard without it sounding like an 80’s song so they just leaned into it instead.
And, man, I tried so hard to make this song feel less '80s, and it just refused. Every time we’d swap out the drum palette with something less old-school, it just lost the vibe. So we just had to admit it. Let it be who it wanted to be.
Amy Winehouse and Bruno Mars have already been mentioned, which were the first two I thought of.
How about Greta Van Fleet?
I’m curious if they sound like a 70’s rock band to someone who has never (at least not knowingly) listened to Led Zeppelin. To someone unfamiliar with Led Zeppelin, you could probably convince them Greta Van Fleet is a 90’s Alternative/Rock band.
See post #2 
. I posted exactly the same video 
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Absolutely nails the '60s, teen idol vibe:
Pretty much anything from The White Stripes or the Black Keys could qualify.
Thr Stone Roses’ ‘Love Spreads’ could have been A 70’s rock song.
The Jayhawks harken back to the Eagles and other melody and harmony driven bands like Poco in the 70’s and 80’s.
Written by Adam Schlesinger of Fountains of Wayne, which could also qualify as a ‘throwback’ group. Sadly, Schlesinger died last year of Covid at the age of 52.
That’s because I was scanning the thread for Amy Winehouse, then I saw that and switched to Bruno Mars, then I thought of Greta Van Fleet and I was well past your post by then.
In fact, I even stopped when you mentioned Nile Rodgers he and Amy Winehouse had worked together.
I guess that Meghan Trainor “All About That Bass” song would count for the whole '60s girl group vibe, although the beat is more of a modern hip-hop sound.
Mayer Hawthorne gets double credit - his solo work has a bunch of '60s soul throwbacks, and he’s also one-half of a retro-funk band called Tuxedo.
Suzi Chunk 2012 - name the era.
Not quite what the OP asked, but this does seem like a good place to mention Postmodern Jukebox. They do modern songs in old jazz, swing, and doo-wop styles.
Never mind. Great minds think alike.
ETA: oh, by the way, Amy and Niles worked together? I had never heard about that. Do you know songs they worked together on?
I don’t think so, at least not that I saw in the 10 seconds I spent looking it up. I just figured if he produced or played on any of her big songs, it would have been worth quoting your Nile Rodgers comment. And it didn’t seem too far fetched that it wasn’t worth a quick google search.
However, Amy Winehouse did work with Mark Ronson, who also did a lot of work with Bruno Mars. Mark Ronson also made this with Erykah Badu, Trombone Shorty and (some of) the Dap Kings. But this isn’t a genre I’m even remotely familiar with. To my ears, it sounds modern, but maybe it sounds older to people that know the style better.
I’m recently obsessed with Fairytale of New York, by the Pogues. It is an eighties song with the sound of an Irish folk song. Fairytale of New York (feat. Kirsty MacColl) [Top of The Pops Dec 1987] - YouTube
Neko Case has a bunch of songs that could have been sung by Patsy Cline in the 50’s.
Weezer always sounded pretty retro to me.
Wolfmother sound like they’re from the 1970s:
Although they usually sound more like 1980s New Wave, Franz Ferdinand’s latest release goes straight back to disco:
And then there’s Muse and their epically retro “Knights of Cydonia” video:
Ah, I see that The Darkness has been mentioned. That video has everything it needs and nothing it doesn’t. Spaceship! Tentacles! Stacks of Marshall amps! Great song!
My contribution is Remi Wolf’s ‘Liz’.
Which is quite unlike everything else I have heard from her. But she also does a decent stripped down live version of ‘Liz’ too.
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I like it. That song doesn’t need a sax. There is absolutely no reason to have a sax in there. But she’s like, fuck it, I’m going to the sax now anyway.
For me, there is a bit of a downside when the first song I ever hear from an artist is one of these throwback tunes. One of the songs previously mentioned in this thread is one of those, and when I heard it the first time I was thinking “Wow, how did I ever miss this?” and looked forward to discovering the decades of music from this artist I somehow never heard. Only to find out that no, such a cache of music doesn’t exist.