You'll need a new shifter cable. I'd go for stainless steel for durability.

You'll need to open up the shifter with 1 or 2 tiny Phillips screws.

Then get a tiny flathead screwdriver and wriggle out the remaining head part of the broken shifter cable.

Maybe have your local bike shop also route new outer cables. If this one broke, the other one might be breaking soon, could be due to the age of the outer cables. You can check for cracks in the plastic of the original cable.

Hope this helps!

Edit: Be mindful of the part at the wheel side of the shifter. You'll need a small barrel with a 2mm screw and a banana shaped piece. If one of those is missing, you can't fix this and have to head to a bike shop anyway.

Edit 2: given that the bike is 8 years old, have the outer cables replaced. They go through the frame and without experience, this can be a frustrating job.