Good pointers there with lone wolf speaking from experience. I’d only add that if the pith in the middle is pink, then it’s a Kentucky coffeetree (Gymnocladus dioicus). If it’s a stand alone tree (the only one that looks like it around) I’d be leaning more towards the coffeetree. Ailanthus will root sprout (part of its invasiveness) and you’d normally see a few more nearby.
I can’t tell from those pics, looking only on my phone that I look at too much and thus gets harder to look at.
But just wanted to note that a friend of mine who gets paid to attack Tree of Heaven regularly suggests NOT cutting them at all but rather applying a strong basal bark treatment to the bottom of the stem. He says this will kill more of the root system and not stimulate as much sprouting as a cut stump treatment will.
Cutting without any treating at all will get you more root sprouts than even Black Locust would send up.
Located in Southern TN. I've been practicing identify trees as I'm working on my property. This one, I'm not having any luck with. Bark is fairly smooth. Compound leaves with opposite arrangement. Can anyone ID it?