HP does not provide a conventional Windows install disc, only customized HP recovery media, which cannot be used in the same manner a regular Windows install disc can.
See this page for partitioning instructions on a HP notebook. HP notebooks have 4 primary partitions, so you have to do a few things before you attempt shrinking the C partition to make space for another partition, read carefully.
HP Recovery has a feature called "Minimized Image Recovery", it will recover the C: partition only, it will not touch any other partitions, but will wipe the C partition during the process, so back up personal data. If you ever need to recover the W7 operating system after creating another partition you will be able to, without disturbing the other partitions.
Make your recovery discs Now, use high quality DVD+R discs or a large usb drive. You can use these to recover if the recovery partition on the hard drive becomes unusable for any reason.
Another option is to make your HP recovery media, then test it to be sure it boots and loads HP recovery manager, then cancel the recovery. Once this is done you can delete/reformat the D: (Recovery) partition to gain a partition to use, you may have to move some free space from C: to D: to get the size you want, I would use a 3rd party partition tool to move free space to D:.