A In Britain, compleat is archaic, used in writing only as a bit of whimsy, and at that rather rarely. It is more common in North America, though often equally whimsical; a quick search of the Web turned up more than 40,000 instances, of which all those I sampled were from the USA.
The Oxford English Dictionary says that compleat is just an archaic spelling of complete. It died out around the end of the eighteenth century. One of its last appearances was a reference to George III in the US Declaration of Independence: “He is at this time transporting large armies of foreign mercenaries to compleat the works of death, desolation and tyranny”. The OED also says that one sense of the word (in either spelling) is the one you quoted — referring to a person who is accomplished, “especially in reference to a particular art or pursuit”.