This depends heavily on which version of iOS it's running, and what the lowest version it's capable of running is. Back in older versions of iOS (I believe up to iOS7) there was a program called "UltraSn0w" that would do exactly what you need. I have not jailbroken a device newer than iOS7, so I cannot say with certainty, but I believe most available jailbreaks on newer iOS versions are rootless, meaning the user is no longer granted superuser privileges by jailbreaking, thus you wont be able to modify the system to perform an unlock with a rootless jailbreak.
With that said it is entirely possible that there are still normal rooted jailbreaking programmes available, I simply don't have experience with them.
If you do choose to jailbreak your iPhone I highly recommend a rooted jailbreak if possible. Contrary to popular belief rooted jailreaking your device is not actually dangerous (at least, not any more dangerous than knowing the administrator account's password on a Mac.). All jailbreaking a device actually does is install the program
su, or "SuperUser", as well as install the package manager
su is preinstalled on all standard copies of Unix, from macOS, to Ubuntu, to good old System III, and is basically just a program for performing administrative tasks like changing the system clock's date, setting the machine to run a program during startup, installing new software, etc. On iPhones, iPods, iPads, and Apple TVs the user can't run the
su program, and is thus unable to do any of the above things without using an Apple app to do it (i.e. the App Store for installing new software, the Setting.app for changing the date, etc.).
When you jailbreak an iDevice, half of the whole process is your jailbreaking program of choice installing a second copy of the
su program in a part of the device's storage that the user can access with normal apps, allowing them to administrate their device manually. While this could potentially be dangerous on it's own, all the access to the
su program is handled through
Cydia.app, which brings me to the second half of a jailbreak.
Cydia.app are both installed during a jailbreak as well,
dpkg is the package manager used by many different versions of Unix, including Debian, and can also be installed on macOS, iOS, tvOS, FreeBSD, and most versions of Linux.
dpkg is essentially just for installing and removing software, and gets installed so that the user can install apps from downloaded
.pkg files, along with the normal
.ipa files used by the App Store, the same way a user can install
.app files manually on macOS.
Cydia.app is basically an alternate version of the App Store that lets you install Linux, command-line, and system software, rather than just Apps. Such software includes, but is not limited to, extra panels in
Settings.app, software that changes the way the SpringBoard (home screen & multitasker) look and work, and Apps that can do things like browse, move, and edit the files on the device how one would with Finder on macOS.
As a result of this process the user can install (or uninstall) most any system software they want, including software that restricts the device to a specific carrier. In order to do this you would either need to find a piece of software for jailbroken iDevices that removes the carrier restriction, or find a way to manually uninstall the software that locks you to its current carrier.
TL;DR It's definitely possible to unlock your iDevice with a jailbreak, but you have to make sure it's a rooted jailbreak (rootless jailbreak wont work), and you'll have to find a program that can be downloaded from Cydia that removes the carrier restriction for you. I believe there is a newer version of the aforementioned UltraSn0w that can do this on newer versions of iOS, but you should definitely look around and make sure such a program exists before jailbreaking the phone, assuming a carrier unlock is your only reason for jailbreaking.