I think you mean "Filter", not "Sort". Sort means to assign a sequence (newer to older or older to newer) to records. What I think you want is to filter out records that don't match the criteria, or put another way, filter in records that match the criteria.
A query on the table in which the NextContactDate (or whatever you called it) is located will return the records you need.
However, there is another logic question that we ought to figure out. What does it mean to say, "... keeping up with outstanding/overdue calls"
How do you know if a call is overdue? Is there another field in the table which indicates you made the call on or before the due date? Or is it just a matter of comparing the current date to all of the date values in the field to see which ones are prior to the current date? I can see this going in a couple of directions, so the following assumption might need to be refined.
I'm going to make the assumption that all you need is a set of records for those clients whose NextContactDate is less than or equal to the current date.
SELECT ClientID, NextContactDate, OtherImportantField
FROM YourTableNameGoesHere
WHERE NextContactDate <= Date()