It looks like /dev/dsk/c1t0d0s4 isn't currently mounted. Can you expand slice 3 to add the space currently allocated to the slice 4, or is slice 4 being used but just not currently mounted?
There are no unused blocks on your disk; all blocks are allocated to existing partitions.
If you want to increase the size of /var and you want to keep it on this disk, you'll have to back up all of the partitions on your disk, reformat it with a larger partition for /var and a smaller partition for one or more of your other filesystems, and then reload the partitions you modified from your backups.
Slice 4 isn't being used, but to make it part of /var it would have to contain blocks adjacent to slice 3. You could merge slice 0 and slice 4 to grow / , but you can't use the blocks in slice 4 to grow slice 3.
You could move slices 0 and 1 to use lower numbered blocks (keeping the same sizes) and and expand slice 3 using blocks no longer being used at the end of the current slice 1 to expand the start of slice 3.
If there is a large directory hierarchy under /var , you could also use the existing slice 4 as /var/subdir (splitting /var into two filesystems). Note that this will only work if there are no hard links between files under /var/subdir and other parts of /var .
Mount slice 4 as /x , copy the current /var/subdir file hierarchy to /x , move /var/subdir to /var/oldsubdir , unmount /x , mount slice 4 as /var/subdir , resolve any differences you find between /var/oldsubdir and /var/subdir (which would only happen if files were being updated in /var/subdir while you were copying the old /var/subdir to the newly mounted partition), and then rm -rf /var/oldsubdir to free up the space that is now duplicated elsewhere.
if it's used as a swap area.
If yes, you may not use it!!
Actually I would look if you can sacrifice the /export/home partition, this seems hardly used and over-dimensioned.
Is there more than one disk in that server? If so, you can use "liveupgrade" to create a new disk layout and after one reboot you are done with resizing everything to your needs...
So you cannot use the slice 4; you would need to delete the swapfile on it, before you can use it for another purpose.
To follow up my idea in using the /export/home, could you run a
du -k /export/home
to see if there is any else data, besides the swapfile.
Well, the most simple plan is to increase /var to 2GB.
With these steps
0. be sure you can login to a ILO, connect to the console, and login as root - you need that only in the case of a system recovery
create another 2 GB swapfile on /export/home, and add it to swap
delete the partition /dev/dsk/c1t0d0s4 from swap
in format -> partition, change the flag from swap to var
create a new file system on /dev/rdsk/c1t0d0s4
mount /dev/dsk/c1t0d0s4 to /mnt
copy over the data from /var to /mnt, using tar or cpio
verify that /mnt looks like /var, then umount the /mnt
in /etc/vfstab, change the /var line from /dev/dsk/c1t0d0s3 /dev/rdsk/c1t0d0s3 to /dev/dsk/c1t0d0s4 /dev/rdsk/c1t0d0s4
9a. in /etc/vfstab, change the swap line from /dev/dsk/c1t0d0s4 to the new swapfile
reboot with "shutdown -g 0 -i 6 -y", keep fingers crossed that it comes up
If this is new for you, you should first practice on a non-productive system.