How do you replace the core of a lock?

Answer 1

One needs to call a locksmith, to remove a lock core requires a core key.

Actually, a locksmith would only be required if the control key for the core is missing...

Interchangeable and removable cores are always combinated or "keyed" outside of the lockable hardware. The control key is integrated into the core's keying to control (hence its name) the retention feature built into the core for the insertion and removal of the core from the lockable hardware. No core can ever be configured with any less than two keys, and at least one of those MUST be a "control"...

Typically, the control key is inserted into the core and, when turned very slightly (it'll stop on its own fairly quickly), it draws in the retention component of the core to allow the core to slip into or out of the prep in the locking hardware. Returning the control key to home position - where it can then be removed - redeploys the retention component. If the core has just been inserted at this point, then it is now otherwise unremovable from within the locking hardware...

IMPORTANT: A core is NOT the same thing as a cylinder. The terms are occasionally misused one-for-the-other outside of the commercial lock and locksmithing fields. If this particular question is in regard to a key cylinder, then removal and replacement would necessitate more details with regard to the hardware in which the cylinder is installed...