Time travel story telling is hard to begin with but when I saw the prompt I could only recall the forward time travel story in Star Trek TNG "A Matter of Time (1991)."

Lol, I wouldn't necessarily recommend this drama, but Melting Me Softly did a travel-forward. Queen In-Hyun's Man is also a travel-forward. The Best Hit I think would also count!!

In Live Up to Your Name, the FL traveled back, but the ML traveled forward.

Tunnel would be my favourite example of this. Rooftop Prince was also a travel forward in time story.

A Time Called You had some back and forth time travelling.

The Devil Judge isn't time travel but it is based a couple of decades in the future.

Rooftop Prince There was a lot of humor but the story was kinda disapointing.

Queen In-Hyun's Man had a nice romance with a smart ML.

Live Up to Your Name was a great drama.

Tunnel was a good police drama.

The most recent traveling forward I've seen is Durian's Affair.

And then Live Up To Your Name. A gem I have heard so much about and it was only a matter of time. Funnily, I was confusing this with another drama having almost the same title, the one about star exchange for a successful music career and starring Lee El in it.
Queen In-hyun's man.

Live Up To Your Name, Tunnel and Queen In Hyun's Man are my top faves.

There was another similar to TSPMC, with two Joseon ladies travelling to the present time. Its called Durian's Affair. The younger couple's story is my fave which is similar to YW and TH. But the rest of the drama can be ignored.

Circle: Two Worlds Connected isn't technically time travel but between the way the story is told with its time jumps and the way the characters are utilized, there's something almost time travel-y about it. Plus the world goes from vaguely present day to The Future capital T-F, dystopia-style, lol.

I think "Tomorrow with you", with Shin Mina has 2 time periods and one is in the (near) future. I may be wrong because I watched it 3 years ago.

I know it’s already been recommended a bunch of times, but I’m contractually obligated to recommend Live Up to Your Name every single time it’s relevant.

One that hasn’t been mentioned as much might be Signal? There is not actual travel but there is a lot of communication across time, and Cho Jin-woong’s character is communicating with characters in the future who can see the effects of his actions playing out in their own world.

The Best Hit!
A first generation idol travels in time to the future (2017).
The FL is the same actress from Park's Marriage. 👍

Queen In-Hyun's Man would be the perfect example for this. It also has one of the swooniest and smartest male lead in the history of k-drama land.

For a different genre, Tunnel delivered a heart warming and heart wrenching twist on the usual thriller/crime drama.

even though briefly, Choi Young traveled to the future to bring heavely doctor (aka kidnap and cut people)

I know these dramas have been mentioned by several beanies, but I come here to show my love for Live up to your name and The Best Hit.
Highly recommended 😊

Reunited Worlds where the ML reappears after 12 years.