The group has been without a full-time chief executive since Mike Hall stepped down in 2016.
Shircore, who joined the group's board in March as non-executive director, was previously an analyst at Phoenix, which now owns 58% of the group.
He said: "With the benefit of a strengthened balance sheet, a much-simplified structure and some of the most knowledgeable and experienced people in their respective markets, we are now able to focus on our long-term future."
Phoenix's UK fund also owns model railway and collectables retailer Hornby.
Stanley Gibbons Group has been restructuring since Harry Wilson took over as chairman in May 2016 with a focus on reducing its debts. The group has sold a number of subsidiaries including its stake in art fair Masterpiece London, auction houses Dreweatts and Bloomsbury and dealer Mallett.
The AIM-listed group now runs stamp business Stanley Gibbons, coin and medal dealer Baldwin’s and auction joint venture, Baldwin’s of St James’s.
In November it announced its investment product division SG Guernsey, which had £12.6m of stamp stock, would be placed into administration. Accountancy firm PwC was appointed administrator.
Last week Guernsey Stamp and Coin Storage (GSCS ) announced it had been approved by the Guernsey Financial Services Commission to offer custody services to store stamps and coins in Guernsey.
It plans to contact investors who own assets in the possession of SG Guernsey. The firm held around 22,000 items for more than 2000 investors on the island. Investors are expected to be given the choice to have their items returned or to store them on the island with GSCS.