The flower stalk won't dry up for a very long time. If seed pods form (sometimes they do, sometimes they don't), you can let them mature till red (takes months), or cut the stalk right down and discard it. It will be full of water, like an amaryllis stalk.

When the pods are very red, should your stalk produce some, cut offf the pod, open it, and germinate the wet seeds in wet paper toweling till they sprout, and plant the sprouts. Yes, they will form cute little clivia plants iin very short order.

Nkt, removing flower stalks opposed to allowing them to remain is mostly done to save berries/seeds for germination.
I too read removing the stalk soon after flowers fade, strengthens the following years buds.

If you want to sow seeds from your Clivia, use the brightest, mosts mature, red berries.

I had an old 10 gallon aquarium filled w/a couple inches of soil. Odds andd ends were rooted inside. One year, I left the flower stalk on until berries reddened. I didn't want to toss them, so I removed each seed, and inserted in the aquarium soil. Months passed, 'can't recall how many,' and baby Clivia seedings grew. When each stood about 7", with 4 or more leaves, I gave them to friends.

Give seeds a try....Toni

Thanks, Toni!

I happened to just pull the stem off instead of cutting since it was pretty loose. Will a new stalk grow?

I was taught to leave the scape (or flower stalk) on the plant until it dries up and can be pulled off with a gentle tug. If you cut the top off when it is still green, you risk having the base rot, and the rot can enter the heart of the plant and kill it. I usually let the seed pods ripen, which takes up to a year in my conditions in the American Midwest. This doesn't seem to prevent the plant from flowering normally the following year. If you don't want to ripen the seed pods, you can just remove them without removing the stalk.