First need to create a new partition and then covert new partition in to lvm partition,After that add that partion in to volume group from volume group add that space to logical volume,Next know what type of ile system it is as xfs format or ext4 format.
fdisk -l
Output
Disk /dev/sda: 85.9 GB, 85899345920 bytes, 167772160 sectors
Device Boot Start End Blocks Id System
/dev/sda1 * 2048 1026047 512000 83 Linux
/dev/sda2 1026048 104857599 51915776 8e Linux LVM
fdisk /dev/sda
Welcome to fdisk (util-linux 2.23.2)
Changes will remain in memory only, until you decide to write them.Be careful before using the write command.
Command (m for help): n
Partition type:
p primary (2 primary, 0 extended, 2 free)
e extended
Select (default p):
Using default response p
Partition number (3,4, default 3):
First sector (104857600-167772159, default 104857600):
Using default value 104857600
Last sector, +sectors or +size{K,M,G} (104857600-167772159, default 167772159):
Using default value 167772159
Partition 3 of type Linux and of size 30 GiB is set
Command (m for help): w
The partition table has been altered!
[root@localhost ~]# fdisk -l
Output
Disk /dev/sda: 85.9 GB, 85899345920 bytes, 167772160 sectors
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk label type: dos
Disk identifier: 0x000639da
Device Boot Start End Blocks Id System
/dev/sda1 * 2048 1026047 512000 83 Linux
/dev/sda2 1026048 104857599 51915776 8e Linux LVM
/dev/sda3 104857600 167772159 31457280 83 Linux
[root@localhost ~]# fdisk /dev/sda
Welcome to fdisk (util-linux 2.23.2).
Changes will remain in memory only, until you decide to write them.
Be careful before using the write command.
Command (m for help): t
Partition number (1-3, default 3): 3
Hex code (type L to list all codes): 8e
Changed type of partition 'Linux' to 'Linux LVM'
Command (m for help): w
The partition table has been altered!
Calling ioctl() to re-read partition table.
WARNING: Re-reading the partition table failed with error 16: Device or resource busy.
The kernel still uses the old table. The new table will be used at
the next reboot or after you run partprobe(8) or kpartx(8)
Syncing disks.
[root@localhost ~]# partprobe
Warning: Unable to open /dev/sr0 read-write (Read-only file system). /dev/sr0 has been opened read-only.
[root@localhost ~]# vgs (To know volume group path)