1st thing, plant a tree underneath in an orientation that mitigates good location on the property and removal of the tree in question without too much interference. 2nd thing, remove the dead portion and probably reduce (probably lighly to start)pthe live portion to help prevent failure in a tree with likely declining structural integrity. 3rd thing, hope for the best prepare for the worst. good luck. if all goes well you get a few years to a few decades of shade while the planted tree establishes. otherwise do the common thing and cut it down and plant a new one. but I like the progressive approach when viable. ideally you utilize staged removal (staged reduction for likely short term as opposed to long term) while shifting the canopy to the new tree. this way you always have some shade, which is not just good for people, but also the young tree. in an exposed setting the old nurses the young to establishment, mitigating wind and drought, as well as growing a less dense, more upright crown for the new tree. basically, mitigating the negative effects of otherwise open grown situations, and instead mimicking the effects found in forest grown situations. and as a derail or a side thought, this is why we need to have more urban areas with several stems in one plot instead of one stem per plot. of course you trade off the aesthetic of a perfectly shaped crown but you gain the advantage of overlapping the generations. you never have an empty spot, or an empty street. just like we should appreciate and consider the cultures of people who have 3 generations of family living under one roof. I wish I spent more time learning from my grandparents before they were gone. in my front yard I planted an Ironwood beside my maple wondering if they are too close. of course they are too close but that's not the point. they are not too close in age and that's good. so once my maple looks like the tree in the pic, the replacement will likely be there. and should the maple go, then it's time to plant another tree near the Ironwood. I know this is in retrospect but looking forward as well. good luck with your tree.
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