In turn, agree evil still existed (5,2)

I believe the answer is:

lived on

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

'existed' is the definition.
(living on is a kind of existing)

'in turn agree' is the wordplay.
'in' becomes 'live' (I can't justify this - if you can you should give a lot more credence to this answer).
'turn' says the letters should be written backwards.
'agree' becomes 'nod' (I've seen this before).
'nod' in reverse letter order is 'don'.
'live'+'don'='LIVED ON'

'evil still' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?

I've seen this clue in the Evening Standard.

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.