Conversion of dream try finished like Socrates (8)

I believe the answer is:

martyred

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

'finished like socrates' is the definition.
'martyred' can be an answer for 'finished' (thesaurus). I'm unsure of the 'like socrates' bit.

'conversion of dream try' is the wordplay.
'conversion of' is an anagram indicator (I've seen 'conversion' mean this).
'dream'+'try'='dreamtry'
'dreamtry' is an anagram of 'MARTYRED'.

Can you help me to learn more?

I've seen this clue in The Independent.

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.