Sim
Can I just take a locked SIM card out and put a new activated one in and it will work with my carrier?
iPhone 11, iOS 14
If what is locked is the SIM card itself with a PUK code, then yes, you can put in an unlocked sim card and it should work. To use a sim card from any carrier the iPhone must also be unlocked for use with any carrier. SIM card lock and device carrier lock are 2 different things.
If what is locked is the iPhone, to a specific carrier, then you will either need a SIM card from that carrier, or request said carrier to unlock the iPhone so it can be used with other carriers. See here: link-> How to unlock your iPhone for use with a different carrier - Apple Support
The device carrier lock would be unrelated to the PUK sim lock.
Link-> Use a SIM PIN for your iPhone or iPad - Apple Support