Modifying SQL 2008/2012 PARTITIONS

You need to alter the partition function.  MSFT gives a decent example here.  Example A splits one of the existing partitions into two, thus creating a new partition:   https://technet.microsoft.com/en-us/library/ms186307.aspx

Or here's a quick example from Kalen Delaney.  The first statements The following statements will create 5 partitions with five different price boundary points:

CREATE PARTITION FUNCTION price_parts (money)
  AS RANGE LEFT FOR VALUES ( 1.00,10.00,100.00,1000.00) ;
GO

CREATE PARTITION SCHEME price_scheme
AS PARTITION price_parts
   ALL to ([PRIMARY]);
GO
SELECT * INTO NewProduct
FROM Production.Product;
GO  

CREATE CLUSTERED INDEX newproduct_pk
  ON NewProduct(ProductID)
  ON price_scheme (ListPrice);


Here we create a table for the partition:

SELECT * INTO NewProduct
FROM Production.Product;
GO  

CREATE CLUSTERED INDEX newproduct_pk
  ON NewProduct(ProductID)
  ON price_scheme (ListPrice);

Run this, you will see 5 partitions:
SELECT * FROM sys.partitions
WHERE object_id = object_id('dbo.NewProduct');

And here you split partition number 3, containing rows between 10 and 100:

ALTER PARTITION FUNCTION price_parts()
  SPLIT RANGE (50);
GO

Look again, you'll see six partitions:

SELECT * FROM sys.partitions
WHERE object_id = object_id('dbo.NewProduct');