Legacy funds are vital to The National Trust. Last year, it raised more than £47m from this source, but is keen to consolidate its position as competition from rival charities grows.
The National Trust is also reliant on income generated from membership fees, which are worth more than £100m a year to the organisation and represent more than a third of its total income.
TDA will begin work on the marketing activity, which is expected to comprise both online and offline member communications, with immediate effect.
Initially, the agency, which was handed the work with-out a pitch, will launch a test campaign targeting one segment of the charity's 3.5m-plus members.
Separately, The National Trust and The National Trust for Scotland are marking Easter with a partnership with Cadbury Trebor Bassett.
The tie-up involves the creation of an 'Easter Egg Trail' campaign. The initiative, which launches on 21 March, will encourage families to visit National Trust sites across the UK to participate in Easter egg hunts over the Easter weekend.
Last month, The National Trust hired BBC Customer Publishing to publish its customer magazine, Active. The Trust is to use the magazine, the first issue of which will be distributed next month, to communicate with its 49,000 volunteers in England, Wales and Northern Ireland.