Once issued, a Police Registration Certificate is valid for the duration of your stay in the UK. It will only expire if you are outside the UK for a continuous period of more than 1 year. This means if you already have a certificate and have not been outside the UK for more than 1 year, you do not need to register again, even if it was issued in another part of the UK, or you were studying at another college or university. Instead you should ask the Police to update the details on it.
Appointments to update your Police Registration Certificate can be booked directly through the Sussex Police Nationality Unit. Please contact them at firstname.lastname@example.org