Succulents can handle any pruning you throw at them and in fact you can replant the piece you remove. It's really up to you.

RL Relocation LLC Since I just moved it to a new pot, do I need to wait a bit. They are already so busy (which I love) and I just don't want to do anything that will cause them to die.

I am wondering about your container - it is very nice and likely suitable for this plant that has tendency to 'trail' - but does it have drainage hole(s)? And the soil looks too water retaining, at least from what is visible in the photo.

If my plant, I would have pruned/beheaded even before repotting, but only if I could supply lots of light. If you can't, plant will grow just the same - it is slightly etiolated. It will always grow longer stems/trunks than many others, but leaves should be compact.

The container does have drainage holes and I got the specific succulent (non-water retaining) soil that was available. I just didn't know if it was okay to leave them growing long like they are.

From the first pic, it looks like Grapetoveria Debbie..but the second pic it looks like it's lost a significant amount of it's colour in four days.

here is a pic from March you can see it's starting to get the pink back.

What ever you do, DO NOT WATER IT again until you see new growth could be up to 3 or 4 weeks. The soil is ok it's the watering you really have to worry about and amount of sun. Where are you located.... can it go outside yet?