The brief covers Lloyds' car, home, pet and travel insurance brands.
Lloyds spends more than £12.5 million a year promoting its insurance brands. However, in the past the majority has been spent on direct mail and door drops.
Andrews Aldridge will develop outdoor, radio, press and online work under the umbrella idea "Our policy is to keep it simple", covering both car and home insurance.
Rainey Kelly Campbell Roalfe/Y&R, which handles Lloyds' above-the-line advertising, has created a direct-response TV campaign.
Andrews Aldridge has worked for Lloyds for three years across its savings, loans, business banking and offset mortgage products.