Hi and welcome, Kate. It should be just fine to use that terra cotta pot for your money tree. I would pitch the old soil that the succulent was growing in, just in case there are residual roots in the soil. Pot up the money tree in nice new sterile potting soil.
But, if you have an indoor cat that likes to nibble on your plants, I'd also advise you to get some cat grass and plant it in that plastic pot that's going to be vacated by the money tree. Don't use the silly little pots they supply at the pet store. If you grow the grass nicely in a pot, it will grow much better, you can plant two pots of grass from the amount of seeds they give you, and maybe kitty will be more inclined to leave your other plants alone.
My daughter grows big pots of cat grass for her two cats all winter on the windowsill, and they love it, sitting like book ends, eating the grass and looking out the window. Wish I had a picture, I'll have to ask her to send me one.