The speed of light is relative. This is why you can never exceed it.

The speed of light is relative to where you are now, not relative to where you started. If, for example, you were going .9999999 percent the speed of light relative to where you started, and you went to the front of your spaceship and pointed a beam of light forward, that beam of light would leave your spaceship at the speed of light. This may be surprising but it’s true. What has changed is your sense of time. If you looked back at Earth you would see everyone going very fast, and if they could see you they would see you going very slowly. Because of this, when you shine your light forward, for you it leaves your flashlight at the speed of your light, 186,000 mps.

This is where relativity comes to play. Out in space there’s no speed limit sign. As far as you know, you’re standing still and the star you’re heading to is coming in your direction. You can accelerate toward it. You could, in theory, accelerate and experience 1G forever without exceeding the speed of light.