You may want to run a Gift Aid Campaign or just report on constituent profiles that do not have a valid Gift Aid declaration, this article runs through the key steps to do just this...

To do this you will need to:

Find and Tag all those with a valid Gift Aid declaration

• Create a Tag, eg. Has a GAD - (Setting Up Tags)
• Create a new Gift Aid Declaration List and ensure that you filter by the correct dates and status' you require. 
• Tag all those on that List with your Tag - (Adding or Deleting a Tag from all Constituents on a List )

You could even set up an Auto-Tag rule to do this automatically so you don't need to manually add the Tag on a regular basis - (Auto Tagging)

Once all constituent profiles are Tagged accordingly, you will need to:

Exclude these constituents from a new Constituent List:

• Create a new Constituent List, filtered by 'Does not Have any' of <your Tag> 
• You can then add additional filters such as Constituent Type equals Individual, etc...

The results will be all those constituents that do not have a GAD on their Timeline.