In his youth, he developed a passion for wildlife conservation and for Rembrandt, which decades later inspired him, respectively, to found the felid conservation group Panthera, and to establish The Leiden Collection, the world's largest private grouping of works from the Dutch Golden Age. At Oxford University, Kaplan earned bachelor's, master's and doctoral degrees in history. He wrote his doctoral dissertation on the Malayan counterinsurgency and the manner in which commodities influence strategic planning. While earning his PhD, he worked as an analyst covering Israeli companies publicly traded in the US. On a Business trip, he met his Future wife, Dafna Recanati (the daughter of Israeli investor Leon Recanati), who had attended the same boarding school as Kaplan. Dafna's mother, Artist Mira Recanati, introduced him to Israeli investor Avi Tiomkin, who hired him as a junior partner in 1991. Kaplan had impressed Tiomkin by correctly predicting Saddam Hussein's 1990 invasion of Kuwait several years before it took place. When Tiomkin decided to concentrate his Investments solely in Israel in 1993, Kaplan moved on to pursue his own entrepreneurial ventures.

Inspired by Marc Faber, who held that precious metals were insurance against the "monetary foolishness" of central governments, Kaplan focused on natural resources investing. In 1993, he founded Apex Silver Mines to capitalize on the improving supply/demand fundamentals of metals. While he was chairman and chief executive officer of Apex, his team discovered and financed the San Cristobal deposit in Bolivia, now one of the largest producers of silver and zinc in the world. Kaplan retired from Apex Silver at the end of 2004 to focus on his new exploration projects.

Kaplan first began investing heavily in gold in 2000. Since the sales of African Platinum and Leor in 2007, Kaplan has focused on the Electrum Group. Its exploration arm, Electrum Ltd., which he co-founded with Dr. Larry Buchanan, owns a Diversified international portfolio of gold exploration assets. Its other entities hold significant interests in several publicly traded companies, including NovaGold Resources Inc. and Gabriel Resources Ltd., two companies that own several of the largest proven gold resources in the world. Among its private interests, the Electrum Group is the controlling shareholder of Sunshine Silver Mining & Refining Corporation, which owns the Sunshine Mine in Idaho, the most prolific silver mine in US history, as well as the Los Gatos silver-zinc deposit in Mexico, which it is developing in partnership with Dowa of Japan.

Kaplan's passion for the Dutch masters began in his early childhood. Kaplan and his wife, Dafna Recanati Kaplan, began to collect the art of the Dutch Golden Age in 2003. Their Leiden Collection is now among the largest private assemblages of Dutch art in the world, and numbers more than 250 paintings and drawings, most of which are included in a free, high-resolution online catalogue. The Kaplans' intention was to establish a "lending library for old masters", including loans for special exhibitions as well as loans to bolster long-term installations.

Kaplan is the executive chairman of Panthera Corporation, a charity which he and his wife co-founded in 2006. Panthera is devoted to preserving the big cats and their ecosystems and has been recognized as a leading force in felid conservation. Conservationist Doug Tompkins has referred to Panthera as "the foremost big cat conservation organization in the world," with National Geographic saying Panthera "represents the most comprehensive effort of its kind in wildcat conservation." For his work as an Environmentalist, Kaplan was the recipient of the "Hero of the Year Award" by the IWFF in 2012.

Kaplan and his wife Dafna helped establish a globally recognized felid conservation program at Oxford University in collaboration with Dr. David MacDonald. In 2009, the couple endowed the Recanati-Kaplan Center at Oxford University's Wildlife Conservation Research Unit, the WildCRU, and the university's Postgraduate Diploma in International Wildlife Conservation Practice, which offers young conservationists from developing countries access to training at Oxford. In February 2012, Oxford's WildCRU was awarded the Queen's Anniversary Prize for Higher Education in recognition of WildCRU's outstanding work in wildlife and environmental conservation.

In March 2014, Kaplan was awarded the rank of Chevalier in the Ordre national de la Légion d'honneur of France, the country's highest civilian distinction. In presenting the decoration, the French Ambassador to the United States, François Delattre, said of Kaplan: "Through your multifaceted life and your support for an incredible array of causes, I believe you are the very definition of a game changer and Renaissance man - a young Renaissance man: as Chairman of the Y, as an Environmentalist in Brazil, as an Entrepreneur, a Historian, a philanthropist, an art collector and a politically engaged individual."

In 2015, after the passing of his boyhood friend, Simon Marsh, Kaplan parted with the two Spitfire Mark I fighter planes that he and Marsh had as partners restored with Historic Flying of Duxford, Cambridgeshire. The first of the planes, Spitfire N3200, was gifted in the presence of Prince william, the Duke of Cambridge, to the Imperial War Museum at Duxford, where it had last flown as the personal aircraft of the Commander of 19 Squadron, Geoffrey Dalton Stephenson, later personal pilot to King George VI. The second, Spitfire P9374, flown by Captain Peter Cazenove over Dunkirk, was sold at auction at Christies London, where it achieved a record price for any spitfire at auction, the proceeds of which were donated for the benefit of the RAF Benevolent Society, Panthera, Oxford's WildCRU and Stop Ivory.

In March 2017, Kaplan was decorated as a Commandeur in the Ordre des Arts et des Lettres by France's Minister of Culture, Audrey Azoulay, at a ceremony at the Louvre Museum. The award was given in recognition of the Kaplan family’s contribution to the arts in France as well as globally.

The Kaplans also founded the Orianne Society, focused on the conservation of the eastern Indigo snake and its habitat, the last remaining long-leaf pine forests of the Southeastern United States. As part of this effort, the Kaplans created the Orianne Indigo Snake Preserve in Georgia through the purchase and donation of 2,500 acres of the snake’s winter habitat. In recognition for their work in wildlife conservation, in 2014 the Kaplans were awarded the New Species Award, and the naming of the newly discovered Orianne's Tree Snake, by the African Rainforest Conservancy.