Curtis, who was chief operating officer and previously led Grayling's public affairs practice, will be responsible for driving growth and best practice across Grayling's nine UK offices.
His new role provides more day-to-day leadership for Grayling's UK operation after Sarah Scholefield was promoted to UK, Ireland and European chief executive last year.
Nutt and Kemp will continue to lead their respective practices but also develop closer collaboration between the agency's UK and Europe offices as part of a new European structure.
PRWeek understands Grayling's corporate practice already has a number of clients with pan-European needs, while on the creative side the UK is regarded as a creative hub that other European offices can better utilise. These new roles formalise the closer working relationship between the UK and European colleagues.
All three will report to Scholefield, who said: "Jonathan has shown great leadership skills and driven exceptional growth throughout his career at Grayling. His new role is critical as we continue to enjoy strong commercial success in our UK business. His role will be primarily focused on maintaining that growth trajectory while overseeing the operational side of the business."
Curtis added: "I'm delighted to be able to take on this new role to work across Grayling, spearheading our ongoing growth across the UK. We benefit from an exceptional team across the entire country and I am looking forward to maintaining our record of delivering excellent work and developing our offer further."
Scholefield said Nutt and Kemp had built strong teams across corporate and Grayling's recently-launched IGNITE creative division, which in November hired M&C Saatchi PR’s creative director Julian Cirrone.
"I have total confidence that they will be successful in extending that success in partnership with our European colleagues and further aligning our businesses across Europe."
Last year, Frankie Oliver returned to Grayling to head consumer brands in the UK and Ireland.
There have been several high-profile leadership moves in the past month, including Weber Shandwick’s Rachel Friend, Golin’s Jon Hughes and M&C Saatchi PR’s Molly Aldridge exiting, and new leaders at MSL.