Transferring an OS from one HDD to another?

So at my work the computer there is 11 years old and the HDD in it is extremely slow. 

I was wondering if there was a way for me to transfer that entire OS from that HDD to a newer, faster one?

I really appreciate any help.

if it's 11 years old it's probably using ide, or possibly early sata, regardless this is the bottleneck, it's entirely possible that the drive isn't performing up to par, however because of the very slow interface i wouldn't expect much, if it's ide have fun even finding a decent replacement drive (if it's sata then it's forwards/backwards compatible, meaning any sata drive will work, but speed will be limited by the interface)

you could also get a pci/pcie expansion card, i'm not sure the specifics of the possible scenarios with that, such as if pci would bottleneck, and if other components of the machine would become a bottleneck

Thanks for mentioning ide. I completely forgot about that possibility. 

Unfortunately it won't be an SSD. They gave me $60 and told me to fix it. And I don't think I can get an SSDfor $60 lol. But thanks for your response.

I'm most likely going to do that. Thanks.