It's not really a real fellowship area, in the sense that there aren't really any practicing "clinical pharmacists" and no recognized board exam. There are PharmD clinical pharmacists as well, which makes things confusing.
There are institutions that offer clinical pharm fellowships for PhD or MD's. These are basically a glorified postdoc and usually involve bench research. There is a board exam you can take, but it's not recognized or administered by the ABIM and costs quite a bit of money, so very few people do it. If you want to pursue a career in basic science research, with or without a clinical research component, clinical pharm fellowship might help you, but I wouldn't do one if your goal is to treat patients.