Can you tell me how to avoid below mentioned exception ?
INSERT INTO [Migrated].[dbo].[Cities] (Name, ZipCode)
SELECT DISTINCT
a.City, a.ZipCode
As @jamieD77 commented you are missing the IsDeleted column in your insert statement.
The error means that the column is marked as "NOT NULL" and therefore a value must be inserted when a new row is created.
So you either need to remove the NULL constraint from the table yourself or insert a value in the column.
INSERT INTO [Migrated].[dbo].[Cities] (Name, ZipCode, IsDeleted)
select DISTINCT a.City,a.ZipCode,0 from [Legacy].[dbo].[Ziplist] as a where (
a.City is not null and a.ZipCode is not null);
For a bit field which I would assume it is (but you should confirm!) the value 0 would be false and 1 would be true. If the field is a different data type these values may have different meanings!!!