How to carry a knife around a kitchen safely?

One should try not to situate the cutting station away from the sink. Most of the time you clean what you are going to cut and you have scraps to put down the garbage disposal. If you need to clean the knife you also need to clean the cutting board.

If I had to carry a lone knife around I would extend my arm down the knife next to my thigh blade pointing behind me. I used to work as a cook and that is how I carried my knife to my station. Coming back I would typically have a number of dirty items so I would just place the knife in the bus tray.

Other way is wrist bent with dull side of the knife against your forearm.

Mistake I see is people want to start cooking before they prep. You start producing dirty pans and use up the prep area and things just go to shit. Here is what I recommend:

1. Clean (and disinfect) the kitchen. Sink counter, pots, and dishes
2. Soak and clean vegetables and fruit
3. Cut / prep vegetables and fruit and put them aside
4. Quick clean
5. Cut / prep meats (if marinade then do that first)
6. Cook - clean as you go
7. One full sanitize
8. Assemble / serve

Typically hold the knife blade flat in the center of the cutting board you used to give a buffer if someone bumps into you and make it clear you have a knife.

If its food, hot pan, a knife or anything let people know you're walking behind them.

I work in a medium sized, crowded kitchen and that's how we are sure to stay safe. Most of the time we don't even have the cutting board just the knife; in that case make it clear you have a knife by holding it moderately up and in front of you, and maneuver it vertically up rather than horizontally or down if you're moving past people and tight gaps. It's easier for everyone to see and notice something up high than down by your waist.

Other than that you can get a knife sheath or an apron with a slot for the knife. (typically aprons only hold pairing knives if any.)

Consider using knives that are pointy AND big at the same time only when absolutely necessary, and carry them point down and/or with non-walkable space below the knife (eg over the counter). If the knife can be SAFELY held at the tip, doing so might be also recommendable.

Try using non-pointy knives as your normal tools if you like large blades: Chinese cleavers, nakiris, tokyo style usubas. They can be held by the blade easily (edge down), and while they can be made wonderfully sharp, they do not have a tip that creates an accidental stabbing hazard (dropping a chinese cleaver on your feet is, of course, inadvisable - tough shoes might be wise). If using something pointy, do take extra care to warn anyone in your path - since that won't happen all the time, attention will be paid.

I have been taught to hold the knife by the handle with the blade against my forearm, sharp edge away from the arm. This way you are hardly likely to accidentally stab someone, and if you trip the instinct is to let the knife go as you try and save yourself. Holding the knife straight down against the leg, if you trip and someone tries to catch you, can result in them being injured by the knife, especially if you forget to let go of the knife first.