Yes I believe so. Any account or equipment change should be requested by the PAH. Since a SIM is a network ID card basically, this would make sense.
Hello there! If the PAH at any point in the past added you on to the account as an authorized user, you will be able to take care of the upgrade yourself. You can do this over the phone, in which case the PAH will need to provide you the PIN/passcode they set up OR you can show a photo ID in the store for assistance.
If you aren't listed as a user on the account, then the primary will have to be with you for any changes you'd like to make.