No, you can't use your Window 7 Home Premium disc.
The first thing you should do is note down your product key. You should find it on a sticker on the bottom of the laptop or in the battery bay sometimes. However, if the sticker is damaged, you can use something like ProduKey to extract the key. Once you have the key, write it down or keep it on a flash drive and store it somewhere safe. There is a way to back up your activation files too but I won't go into that.
Also, you may want to back up your drivers with something like DriverBackup! to make it easy to reinstall your drivers. Otherwise, you can go to the manufacturer's site and download the drivers for your computer.
To summarize, you have 3 options:
a. Clone the hard drive.
b. Create a Windows 7 Professional ISO from your Windows 7 Home Premium disc.
c. Download a Windows 7 Professional ISO.
Of the three, c is probably the easiest option so I only deal with that one here...
1. Follow the instructions in this article to download a Windows 7 Professional ISO from Microsoft Tech Bench. There is no telling when this workaround may stop working, so you should act quickly.
2. Once you have the ISO, go to MSDN Subscriber Downloads and use the box that says "Enter a Product Name" to search for the same ISO.
3. Once you find the matching listing, click on the link that say "Details" to expand the listing. (Note, you won't be able to download anything at MSDN without a subscription but we just want the SHA1 hash).
4. Locate the SHA1 hash and use something like Hasher Lite to compare it with a SHA1 hash of the ISO to make sure they match. This will ensure that the ISO wasn't corrupted in the course of downloading.
5. Next, follow this article to make a bootable Windows 7 USB flash drive with Rufus.
6. Install the new hard drive.
7. Insert the flash drive and boot your computer.
8. Follow the prompts to install Windows on the new hard drive. You may need go into the BIOS to change the boot order if the computer doesn't boot from the USB drive.
9. Install your drivers.
Let me know how it goes.