Hi Alistair,
To earn M365 Administrator Expert certification you must pass MS-102 and have at least one of the five prerequisite certifications Active.
If you don't have at least one of the five prerequisites then you just need to pass one of those exams within 1 year of passing MS-102 and both certifications will show up. If you do have one of the required certifications and it is Active, then please check your Certifications tab.
If the certifications are not on your certifications tab you will need to ask question in Microsoft Credentials forum. You may use link below:
https://trainingsupport.microsoft.com/en-us/newthread?threadtype=Questions&forum=mcp
Please click Accept Answer if the above was useful.
Thanks.
-TP