Yes. The closer to light speed you're traveling, the more time dilation there will be. Though getting up to such speeds is nearly impossible. No particle that has any mass can ever reach the speed of light. It would take an infinite amount of energy to accelerate to the speed of light. So we'll have to settle for 99.9%. I also don't know when time dilation starts to occur. Is it ever-present or is there a certain speed you have to reach? If I'm driving down the road, how does relativity compare someone sitting on their couch? For every 60 seconds in the outside world, do we both experience 60 seconds of time? Or do I experience 59.999999999999999999999 seconds? Obviously time dilation is exponential with the speed of light as an asymptote, but when does time dilation kick in? When do the laws of physics start worrying about how fast you're going and start time dilating you? I don't think I've read this anywhere. Edit: I totally forgot about gravitational time dilation. Time travels faster in less gravity than it does in heavier gravity. Like if you were being sucked in by a black hole you would see the rest of the universe zipping by in time. I haven't thought about time dilation for a while if I forgot this aspect of it. Like if humans could somehow live on Jupiter their average life expectancy would be longer than ours simply because Earth time would be moving quicker relative to Jupiter time.
This might sound crazy but I've heard theories about it that had some merritt. But if you could some create a wormhole (essentially a bend or a shortcut in space) physics wouldn't really apply. Idk if that would just mean we could cover billions of light years in an instant or if time would be affected. It's an interesting thought. But obviously completely hypothetical.
There's also a concept of riding spacetime like a wave in order to achieve faster-than-light (FTL) speeds. From our observations so far, space doesn't have a speed limit like the rest of the universe. If you could manipulate it to where you would simply move space instead of matter, FTL is theoretically possible. Otherwise like I said before, you can't accelerate matter to light speed or beyond. The only way to achieve those speeds would be to hop a ride on a space wave.