We pulled out a tree and the roots are now decomposing causing our lawn to sink.
How do I fix this?

Thanks

I know that this can be a problem because when the ground is sinking it can be a hazard that people may trip over in the dark. Also, certain types of bees love to nest in any holes or air pockets that are left.

If the roots are decayed enough that they have become really soft, you might want to try tilling up the are with a type of tiller that rotates really fast, like a Mantis Garden Tiller. Smooth out the dirt with a rake.. See how level/smooth it is. May need to fill with dirt and plant grass seed or lay some sod.

If the roots are not soft enough to do the above and without doing a lot of digging by hand to remove the roots, I would just fill in with dirt and add grass seed, maybe clumps of sod where they fit. Might need to keep doing this as the roots continue to decay.

I have the same problem in my front yard from a big, old tree that was cut down years ago. I just keep filling in the sunken spots.

I have filled the spots with potting soil in hopes the grass will fill in and level out the
Area where it sunk. Do I need to add grass seed? This is a tall fescue sod lawn.

If it is a tall fescue, it should spread. How soon, depends on the type. You mention filling in spots, which makes me think that you are filling in small areas. But, please correct me if I'm wrong.

If the areas are large you may want to plant some seeds.

My areas are small. I usually don't plant any grass seed because the grass spreads and fills it in fairly quickly.

The following site may be of use to you. I hope that it is.

Tall Fescue for Forage Production

It is a small area. I am hoping this will work. It is not only a safety issue, it
Is does not look good as well. Thanks for your answers.

You are welcome and thank you!

Your potting soil fix is actually quite good. The roots run everywhere so you probably can't dig them all up, you'll miss one. The roots will keep rotting for a few years, add some soil and seed twice a year. Just wait until the mushrooms start growing, they like to follow the root lines.