I would combine the vehicles, entities, and enterprises tables into one table. Add a field to this table that indicates which type each record is. This will eliminate at least 4 tables from your current design and simplify your query.
That said, here is an example query to get 'enterprises' with a DateTo that is less than the current date, presumably these are expired.
Code:
SELECT TblPeople.PeopleID,
TblPeople.FirstName,
TblPeople.Surname,
TblPeople.[Prof ID],
tblEnterprises.EnterpriseID,
tblEnterprises.Enterprise,
tblPeopleEnterprises.DateTo
FROM TblPeople
INNER JOIN (tblEnterprises
INNER JOIN tblPeopleEnterprises
ON tblEnterprises.EnterpriseID =
tblPeopleEnterprises.EnterpriseID)
ON TblPeople.PeopleID = tblPeopleEnterprises.PeopleID
WHERE (( ( tblPeopleEnterprises.DateTo ) < Date() ));