Old nurse had my pill that we must dissolve (4,4,3,4)

I believe the answer is:

lady with the lamp

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

'old nurse' is the definition.
(I know that Lady with the Lamp is a nurse)

'had my pill that we must dissolve' is the wordplay.
'had my pill that we' can be anagrammed to 'LADY WITH THE LAMP'.
Though, I am not sure how the anagram is indicated.

Can you help me to learn more?

I've seen this clue in The Times.

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