Sorry the code submitted includes reference to the superseded column which in not relevant to this question. Only this is needed:

CREATE TRIGGER [dbo].[AddSpecificationID]
   ON  [dbo].[Specification]
   AFTER INSERT
AS 
BEGIN
    SET NOCOUNT ON;
    Update Specification
    Set SpecificationID = EntryID 
    where isnull(SpecificationID,0) = 0
END
GO

This worked on MS SQL