Potential issue with city tree

I'd like some advice from some knowledgeable neighbors.  I happen to live close to a busy street, and on the busy street is a large tree.  I love the shade that it provides.

My issue is, I think the tree's roots are growing underneath my yard and shifting some of my pavers.  Is there anything you can think of that might help me resolve the issue?  Do I have to go to the city to ask them to remove the tree?

Again, I love the tree and the shade it provides, and would hate to see it go.  But I also don't want the tree's roots to damage my property.  Any advice you can offer would be very much appreciated!

I'd research if it's a City tree or an HOA tree. Although it might be on what appears to be City property, it may be an HOA responsibility.

Once roots travel to your property you should be able to do with it what you want. Working under that supposition, I'd hire an arborist/tree surgeon and get a written opinion on how to mitigate the problem. Once in hand, go to the City/HOA and get their opinion - don't ask the City/HOA first or they may cut down the tree - go in ready and you might get the approval or acceptance of your plan so you can deal with it. Don't wait for the City/HOA to fix it because it will likely be delayed or incorrectly dealt with.

My .02c