Old PM cheers toothless types (8)

I believe the answer is:

edentata

I'm a little stuck... Click here to teach me more about this clue!

'old pm cheers toothless types' is the definition.
I can't judge whether this definition defines the answer.

'old pm cheers' is the wordplay.
'old pm' becomes 'eden' (Anthony Eden, UK prime minister 1955-1957).
'cheers' becomes 'tata' (both can mean goodbye).
'eden'+'tata'='EDENTATA'

Can you help me to learn more?

(Other definitions for edentata that I've seen before include "mammals" , "Group of creatures" , "toothless animals" , "Beastly group" , "there are various animals in it" .)

I've seen this clue in The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.