If your Venus flytrap plant was shipped to you bare root, it’s normal for older leaves to begin to turn brown and black after transplanting. It’s easier for the plant to re-establish itself if it has fewer leaves to support while its roots are becoming accustomed to the new medium and growing conditions.
If the Venus flytrap came potted, it’s likely just suffering from any climate change it’s endured during transit. Don’t worry! Just trim off any parts that turn black and it should begin showing new growth soon.