This is a bit extensive to discuss in a forum like this, but...
Generally I do this by importing the data to a work table (not the one you want the data to end up in). It should also have it s own identity column (Useful for separating out duplicates within the data) and a column for your database table record id. Hopefully the data has some type of id field for each record. If it does, then you should have a mapping table that links the datbase ids from your database to the record ids from the Access database. Then it becomes a simple matter of looking for the ids that don t exist in the mapping table and inserting the records associated with them your the production table you are putting the information into. Usually when I do this I add my own id field to the work table and then I insert those records into the mapping table as a final step.
If the data you are receiving has no id field, this is much harder and may be impossible depending on the nature of the natural key or even if you have one (Access databases often being notorious for not following database design principles). If the closest thing you have to a unique identifier is the name/address combination how do you know if John Smith at 10 State Street in Chicago IL is the same person as John Smith at 25 Main Street Chicalgo , IL. He could have moved or it might be a differnt John Smith.