Chief executive Norrie Stewart will step into the fold until replacements are found.
Gavan and Clements had responsibility for finding new sites and overseeing logistics to support expansion.
A source close to the business said the pair were likely to be replaced, but it is unclear when appointments will be made.
The MBO team, which was led by Stewart and included Gavan and Clements plus finance director David Milton, was backed by a private equity syndicate led by Penta Capital and Barclays Scottish Leveraged Finance in September last year.
Stewart, who at the time of the buyout had worked at women’s young fashion chain Internaçionale for 11 years, took a near-20% stake in the deal. The rest of the management team – Milton, Gavan and Clements – shared 25% of the equity.
Internaçionale appointed Sue Scanlan as its first managing director earlier this year. She joined after working at Primark in an interim role.