The agency’s new practice, launched in the wake of campaigns about the gender pay gap and proxy voting in Parliament, as well as movements such as #MeToo, will work with people and organisations to accelerate female empowerment.
It will work inside organisations to achieve genuine empowerment and culture change, rather than tick-box representation.
The team will also push for positive change for women by celebrating their unique needs and differences, the agency said.
Jess McVey, a senior account manager in the practice, said: "It’s now over 100 years since women won the right to vote, yet gender inequality is still rife. Women remain underrepresented in politics and underpaid in the workplace."
She added: "We want this practice to address those issues and more. We will work with people and organisations that share our desire and vision to help accelerate change, remove barriers and alter perceptions."
Empower’s founding members include WealthiHer, a campaign to make the finance industry more female focused, backed by HSBC, Barclays and J.P. Morgan, as well as Blackheath High School.
Tamara Gillan, founder of WealthiHer, said: "Higginson’s reputation for championing gender equality precedes them and their passion for empowering women is so evident every time I speak to them...We couldn’t hope for a better partner to influence change."
The practice will be officially launched in Parliament on Monday at an event hosted by Labour MP and women's rights campaigner Jess Phillips. She will be joined by anti-'upskirting' campaigner Gina Martin and Netmums founder Siobhan Freedgard.
The event will explore whether social media has helped or hindered female empowerment.
Empower will meet quarterly to discuss ways of promoting female empowerment and will host two annual events, as well as recording three podcasts per year on relevant issues.
Meetings will begin next month and the first podcast, to be released on International Women’s Day (8 March), will feature Phillips.
The second event will be held in November, on the topic 'The Future of Work'.
Smith, who was only the third woman in British politics to hold one of the great offices of state – prime minister, home secretary, chancellor and foreign secretary – was also deputy minister for women during her time in Parliament.
She served as the UK’s first female home secretary from 2007 to 2009 and joined Westbourne Communications to chair its public affairs practice in 2015.
Commenting on her new appointment, which is a part-time role, Smith said: "Empower will support organisations and individuals championing women in all areas. Increased representation is important, but just the first step. We want to achieve real impact through celebrating the skills and perspective that women bring."