Welcome to the forum honey
If your licence was issued before 1st February 2001, then you can ride a 50cc moped, capable of not more than 30mph. Strangely enough, you will not need to display L plates, and you can carry a passenger if the motorcycle has a passenger seat and rear footrests. If you want to ride a motorcycle of over 50cc, up to 125cc, you must take Compulsory Basic Training (CBT), you must display L plates, and you must not carry passengers. The CBT certificate is valid for 2 years.
If your licence was issued after 1st February 2001 then you will need to take Compulsory Basic training (CBT). Once you have completed this course, you will be able to ride a 50cc moped without L plates, until your licence expires at age 70, and you will also be able to ride a motorcycle of up to 125cc with L plates (no passengers allowed) for 2 years from the date you completed the CBT course.
Hope this helps.