Yeah looks right to me, although that in no way precludes it from being something else. Especially TX that has a rather unique flora.

Just came to me. Bumelia was what I think thinking of...only a very general sense of it being a BLE with simple alternate leaves as well.

The very light-gray stems say 'Yaupon' to me.

No, I don’t think it’s a Yaupon Holly, I’ve had many of them for over 25 yrs (D/FW area) and it just doesn’t look like one to me. Was there a mother tree nearby?

I wondered about Ilex glabra, but don’t have enough experience with them to know for sure. There are so many Ilex varieties in Texas.

I think you should at least consider Yaupon. Here’s a pic of mine now. Note reddish petioles and terminal twigs, and light gray stems on older growth. Leaves have scalloped margins. Evergreen. Often shrubby, but can make a small tree. Super common landscaping plant in Texas.