Flying creature that could shift to protect lady (11)

I believe the answer is:

pterodactyl

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

'flying creature' is the definition.
(I've seen this before)

'could shift to protect lady' is the wordplay.
'protect lady' anagrams to 'PTERODACTYL'.
Though, I am unsure how the anagram is indicated.

'that' acts as a link.

Can you help me to learn more?

(Other definitions for pterodactyl that I've seen before include "Flying dinosaur" , "Late Jurassic flyer" , "Fossil flyer" , "Winged reptile of old" , "Extinct flier" .)

I've seen this clue in The Times.

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