I'm guessing it needs fertilizer. Woody stems are said to be a sign of potassium deficiency. If the leaves are dull, it probably also needs more nitrogen. If the leaves are purple, it probably needs phosphorus.
New potting soil doesn't always come with many nutrients.
Getting growth from a stump is not assured, even if you do everything right (I assume the base has no leaves. If it does, just treat it normally and it'll be fine). I hope it was actively growing before you cut it
If it's outside, I'd put it in an area with less harsh, filtered light. If it's inside, I'd just do normal culture. As for water, just water it ...