After a bit of trial and error... as mentioned in the possible answers, it turned out to require xfs_growfs rather than resize2fs.
CentOS 7,
fdisk /dev/xvda
Create new primary partition, set type as linux lvm.
n
p
3
t
8e
w
Create a new primary volume and extend the volume group to the new volume.
partprobe
pvcreate /dev/xvda3
vgextend /dev/centos /dev/xvda3
Check the physical volume for free space, extend the logical volume with the free space.
vgdisplay -v
lvextend -l+288 /dev/centos/root
Finally perform an online resize to resize the logical volume, then check the available space.
xfs_growfs /dev/centos/root
df -h