Several HDD makers will give you a cloning utility for free by download from their website. The trick is this: they customize their utility to make a clone only TO one of their drives. That is an inducement to buy from them. So, if your NEW larger HDD if from Seagate, get their utility Disk Wizard. If your new HDD is from WD, get their Acronis True Image WD Edition. Whichever you get, install it on your existing C: drive, then run it from there to make the clone onto the new drive.
That assumes you can connect both units to the same machine, your laptop. If you can't, you'll need some way of connecting them both to some other machine temporarily and installing the cloning utility package so you can do the job.
When you do the cloning, be absolutely sure that you designate the Source and Destination drives correctly. The process completely wipes out any old data on the DESTINATION drive, so be sure it is the empty new one.
Now I have a hint for your specific question. Several I've used have this behaviour in common. They analyse the info and propose a a group of settings for the job, and ask you to approve before proceeding. Do NOT blindly hit Enter every time. Often I find they propose to make the Partition on the Destination drive that it will create to receive the clone the SAME SIZE as on the old drive! You should NOT approve this, and use the menus to change that to make the new Partition on the new drive as large as it can be - all of the new drive's space. For this reason, I always recommend you get and READ the software documentation. You will find it does LOTS more than just cloning, and there is probably a specific chapter on cloning where you'll find the details of the settings you can adjust before approving them.