My license is set to expire in a couple of days. I know there is a grace period but I'd like to know if I were to take an exam after the grace period I would be reassigned the same callsign or a new one?
The grace period is two years.
You can renew your license within the grace period, but after that, the call sign will be available for reassignment.
If you were to take and pass an exam after the grace period, you would be assigned a new call sign. However, if at that time, your old call sign is still available, you would be able to apply for it as a vanity call.
There are certainly no guarantees, but if your old call sign was an automatically-assigned one, and not, say, a desirable 1x2 or 2x1, it will likely still be available for quite some time.
Just as an example, my father-in-law passed away in 1990 and no-one notified the FCC, so the license expired "naturally" in 1998. About a year ago (2019) when I got my General license, his old call sign was still available, approx. 21 years after it expired, so I applied for his call sign, and got it.