Is it normal to "commission" an artist for a design?

So I have a quarter-sleeve on my arm that I'm not really content with anymore. More specifically, I don't really like the background on it and would like something a bit more detailed but I don't have exact designs in mind. I thought this would be a cover-up at first but I wasn't so sure since it's not really covering anything up. Rather than browsing through dozens of portfolios at tattoo shops, I was hoping that I could just give a general theme or idea for my desired design to an artist that I trust and have him/her draw a design for me. What would this be called and is it normal to ask an artist for this? Obviously, I'm aware that this should cost some amount of money as well and I'm fine with that. If anyone on here can help me out, I'd greatly appreciate it! https://ift.tt/2Zigp6g