That's a VERY good question.
The easiest way out is to leave the current partition as it is, and make a new one covering the now unallocated space. Then you end up with a 137 Gb partition and a 350 Gb partition: two drive letters on the same physical disk. That's no real problem.
Once you've done that, it needs some optimizing, because FAT32 is less reliable than NTFS:
1. Copy all files from the old to new partition (and delete them on the old).
2. Use the Windows XP program convert to change the old partition from FAT32 to NTFS. See http://www.aumha.org/win5/a/ntfscvt.php (but use the correct drive letter!).
3. Move back what you like, depending on your plan to organize your data in 2 partitions.
And an important remark about backup. If you browse our Storage Forum, you'll find an amazing number of posts from people losing data on their external hard disk. So be sure you've got a backup of everything that's on it and that you don't want to lose. The recommended way to store all those backup gigabytes is, of course, a second external hard disk! But a BlueRay burner should work also, with 50 Gb on one disk.