Launch a stored procedure when a datetime is expired
You should create a SQL Agent job. This can poll your column and fire your stored procedure when the datetime exceeds a specified value.

Alternatively, if your stored procedure needs to run at exactly the specified time, schedule a SQL Agent job to fire at that exact time and don't poll. You can do this programmatically via the sp_add_jobschedule system stored procedure, or manually depending on your requirements.

Using the latter method you could remove the logic that writes the desired time to a table. If that table value is still required however, you could create a trigger on that table that invokes sp_add_jobschedule to create a job schedule.