Am a saint, having converted island (8)

I believe the answer is:

tasmania

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

'island' is the definition.
(Tasmania is an example)

'am a saint having converted' is the wordplay.
'am a saint' can be anagrammed to 'TASMANIA'.
Though, I'm not clear how this is indicated.

Can you help me to learn more?

(Other definitions for tasmania that I've seen before include "mountainous island" , "Aussie's state" , "Australian island to south of Bass Strait" , "somewhere in Antipodes?" , "State off 23 [VICTORIA]" .)

I've seen this clue in The Times.

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