Gill, the company's former group events director, has stepped in as interim CEO. He will be tasked with creating a clear strategy for the business and building on Dunleavy-Bell's work, which saw Concerto report an increase of 123% in profit before tax in the period ending February 2014.
Gill will remain non-executive chairman of Story Events, the company behind events including The London Christmas Party Show and London Summer Event Show.
Information regarding the next move of Dunleavy-Bell, who was ranked fourth in the Event 100 Club 2015 installment, is yet to be revealed.
She explained that the business is now in "healthy shape", and is subsequently ready for a new challenge.
Dunleavy-Bell said: "I came here three years ago to help the shareholders shift Concerto from a good lifestyle business to a great professional group. We had some big commercial challenges and have overcome these through consolidation, targeted acquisitions and investment in great people.
"The results speak for themselves. We have made a serious improvement in the profitability of the business, reporting triple digit growth in profit in the first year. The results for 2015 will show sustained improvement."
David Gilbertson, chairman at Concerto Group, added: "TA has brought a professional rigour and results focus that has driven the business to materially improved profitability. She is passionate about helping businesses move to the next level and while sorry to see her go, we support her wish to take on other similar challenges."
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