It's possible, but the design of your database and when/how you want your reminders to appear make a big difference in how this would be set up.
One way is to set up a script that is performed every time you open the file. The script can perform a find, entering criteria in that next contact date field and listing any found that meet criteria specified in the script. It might find all records where the date is the same as today, a day in the future some time this week, next week, or ...
That refreshed my memory enough to sort out what I need to do.