There is another question to consider here. You do not say whether the HDD you are considering is IDE or SATA. If it is SATA, you have no problem at this stage, so you can skip to my next paragraph. BUT if it is IDE, then you must first find out whether your laptop's IDE system (via the BIOS) has a feature called "48-bit LBA Support". (All SATA systems have this - it's just IDE systems where this can be an issue.) Just "Support for large hard disks" or "LBA Support" is not enough. It must specify the "48-bit LBA" part, or specify that it can support disks over 128 GB. If in doubt, try to contact Tech Support at the laptop manufacturer's place for advice. If you cannot get 48-bit LBA Support established in your laptop's hardware for an IDE drive, then you WILL have to limit yourself to using no more than 128 GB (Windows' way of counting) of that drive.
If you don't plan to slipstream a Service Pack and make a new XP Install disk that way, you can still work with just your original-version XP Install CD. Just follow these steps. You will end up with a fully functional HDD, BUT it will be divided into TWO Partitions, each treated by Windows as a separate "drive".
1. Install the 160 GB HDD unit and proceed with a normal Install of Win XP from your old CD. Near the beginning if necessary, use the menu choices to Delete any old existing Partitions on the drive, then go ahead. The Install process will ask you to confirm the location and size of the Partition it plans to Create on your HDD, and I'm sure it will NOT propose anything over 128 GB. Set the size to whatever you like, not exceeding that limit. Install will create the Partition, Format it, and Install Win XP. Now your system is working fine. At this point there is about 20 GB of Unallocated Space on that HDD (or maybe more if you made your Boot Partition smaller).
2. IF you know you have 48-bit LBA Support on your machine's IDE system, or IF you are using a SATA HDD anyway, you can now prepare to use the rest of your HDD's space. Do NOT try to do this if you don't have that 48-bit LBA Support feature. At this point you need to add that feature to your Win XP OS by installing a Service Pack. You should download and install Service Pack 3 (the latest) BEFORE trying to use the extra space.
3. OK, with XP updated to SP3, you reboot and use a Windows built-in tool called Disk Management. I get there by clicking on Start at lower left, then RIGHT-click on My Computer in the mini-menu and choose Manage. In the window that pops up, choose Disk Management. On the right will be two panes, and each of them SCROLLS to let you see all it has. Focus on the LOWER RIGHT pane where you will see several rectangles representing the drive units in your machine. At the left-hand end of each rectangle is some label info like a disk name and type, its total size and a status. To the right of that there are one or more sub-blocks, each representing a Partition on that HDD unit. Within each Partition block there will be more info, like the name you assigned to this Partition, its letter name, the Partition size and File System, and a status. On your 160 GB unit there ought to be a block of 128 GB (or less, depends on what you chose) as your C: drive, and to the right of that a block labelled "Unallocated Space". RIGHT-Click on that and choose to Create a new Partition from that space. This one should be a Primary Partition also, but it does NOT need to be made bootable. You may see also some options for the Format operation. These include the File System to be installed (choose NTFS), and whether to do a Full or Quick Format. Since you are re-using an older HDD, I suggest a Full Format. It will take some time - an hour or more - but it's a good precaution to have the drive tested that way. When the job is done it will have its own new letter name assigned. Back out of Disk Management and reboot to update the Registry. The 160 GB unit will now show up in My Computer as a C: drive of (maybe) 128 GB, and a second "drive" (probably E:, since I suspect your optical drive will be D: ), and you can use both of them.
As I said, do not try to create a Partition from the Unallocated Space unless you have 48-bit LBA Support in the laptop's disk controller and in an updated version of Win XP. Doing that without 48-bit LBA Support and using it can create an odd situation in which attempts to write to it are actually performed on the beginning part of the HDD, instead of the end, thus over-writing and destroying data you need.