Best way to increase no of partition in SQL Server Table
It sounds like what you want to do is to create a new boundary for your existing partitioning implementation, and this can be one through ALTER PARTITION FUNCTION ... SPLIT RANGE ....  

You will also need to run prior to this an ALTER PARTITION SCHEME ... NEXT USED ... to indicate the next filegroup that will hold the new partition (there are a few caveats to this, as quoted below).  Here is a quote from BOL regarding this operation:


  A filegroup must exist online and be marked by the partition scheme that uses the partition function as NEXT USED to hold the new partition. Filegroups are allocated to partitions in a CREATE PARTITION SCHEME statement. If a CREATE PARTITION SCHEME statement allocates more filegroups than necessary (fewer partitions are created in the CREATE PARTITION FUNCTION statement than filegroups to hold them), then there are unassigned filegroups, and one of them is marked NEXT USED by the partition scheme. This filegroup will hold the new partition. If there are no filegroups marked NEXT USED by the partition scheme, you must use ALTER PARTITION SCHEME to either add a filegroup, or designate an existing one, to hold the new partition.