Blower has been with the firm for 11 years, arriving as an account executive, and previously worked for Defra, a Democrat Congressman and an MP in Westminster. She returned from maternity leave in June.
Hanover has promoted two other members of the public affairs team, known as UK Advocacy, to director to support Blower: Rosie Luff and former Conservative special adviser Daniel Gilbert. The team's other director is ex-Labour adviser Rhoda Macdonald.
Three individuals - Emma Dean, Tom Gault and Alison Woodhouse - have been promoted to associate director.
Swire will continue to support Hanover, with a release saying she would "step back from day-to-day management, taking on a role as senior adviser within the firm".
She has been with Hanover for ten years, leading UK Advocacy for the last four and overseeing it doubling in size. Clients include Sky, Tesco, Facebook, Microsoft, Airbus, Lucozade Ribena Suntory, Goldman Sachs and Tata Steel.
The news comes three weeks after Hanover acquired the Middle East business of Bell Pottinger.