Q.LAWN GROWTH
My lawn has disappeared about a meter around a tree that my wife planted at the edge of the lawn a few years ago, what grass (if any) can I plant to overcome this situation?
I would visit your local garden center and inquire on the best shade grass for your region.
Growing grass under trees is an issue for many home gardeners.
You may also want to consider a shade ground cover as an alternative to typical grass.
Here are some articles with more information.
https://www.gardeningknowhow.com/ornamental/trees/tgen/tips-for-growing-grass-under-a-tree.htm
https://www.gardeningknowhow.com/lawn-care/lgen/growing-grass-shade.htm
https://www.gardeningknowhow.com/ornamental/groundcover/gcgen/ground-covers-under-trees.htm
https://www.gardeningknowhow.com/lawn-care/lgen/shade-tolerant-grass.htm