Law joined the agency this week and has been tasked with developing the shop’s strategic planning direction.
He will report into Neil Miller, the chief executive at Possible, who joined the agency in February.
Prior to his five years at Fabric, Law was the head of planning at TBWA\London for a year and nine months. He was also the group planning director at WCRS from 2006 and 2008 and has previously worked at Goodby Silverstein & Partners and SapientNitro.
Law said: "One of the big things that swayed me to join Possible was meeting the team and seeing the passion Lucas, the executive creative director, brings to the creative offering.
"Having met Neil 20 years ago when I was at Saatchi & Saatchi, I’m now looking forward to working together to build a famous digital agency.
"After the past few years at the coalface of data, this is the opportunity to further build a department that truly fuses data and planning to drive strategy focused utterly on creative results."
Law will work alongside Mandhir Gidda, the chief technology officer, and Christiaan Lette, the client services director.
Miller said: "Simon is the latest in several strategic leadership appointments at Possible. Bringing in these key players to the agency means they will be able to share their rich knowledge and experience with the team and clients.
"Simon has great expertise in creating tech and marketing opportunities based on current trends, and is perfectly placed to translate these into effective solutions for clients.
"It’s an exciting time for all at the agency as we seek to continue our growth in the market and offer clients truly innovative campaigns that solve real problems."