Creating non-clustered Index on Partitioned Table that already has an existing Primary Key
Since the TABLE_A is partitioned on COL_1, the new Primary Key being added must include COL_1 as part of it. 

So the PK ends up being created as so:

-- Add the MY_KEY column 
ALTER TABLE dbo.TABLEA
ADD [MY_KEY] UNIQUEIDENTIFIER ROWGUIDCOL DEFAULT NEWSEQUENTIALID() NOT NULL

-- Create the PK constraint 
ALTER TABLE dbo.TABLEA
ADD CONSTRAINT PK_TABLEA PRIMARY KEY CLUSTERED (MY_KEY,COL_1)