It is the first time that Lucky Generals, which celebrated its fourth anniversary last month, has had one person dedicated to new business.
In addition, Tate will be in charge of seeking international opportunities and new capabilities.
Lucky Generals said it is "likely" that a new-business director will be hired to report to Tate.
Reporting to co-founder Helen Calcraft, Tate starts on 19 June.
Tate is not taking an equity stake in the company. Lucky Generals sold a majority stake to Omnicom’s TBWA in February.
After ten years at Mother, Tate announced in 2016 that she would not return after completing her maternity leave. She joined the independent agency in 2007 as strategy director, working across Coca-Cola brands. She was appointed its first managing director in 2013.
Before Mother, Tate held planning roles at Bartle Bogle Hegarty and Abbott Mead Vickers BBDO.
Calcraft said: "Sara has a formidable commercial brain and strategic intellect that will serve us well as we grow."
Danny Brooke-Taylor, Andy Nairn and Calcraft, the founders of Lucky Generals, retain a significant minority stake in the agency, which sits alongside TBWA\London in the new TBWA UK.
Lucky Generals has not taken on existing TBWA clients but works alongside the network on fresh new-business opportunities.