Medic, old, got lost wandering around island (9)

'medic' is the definition.
The answer and definition can be both people as well as being singular nouns.
Maybe you can see an association between them that I can't see?

'old got lost wandering around island' is the wordplay.
I cannot quite understand how this works, but
'old' could be 'o' (common abbreviation eg in OE for Old English) and 'o' is present in the answer.
'lost' could be 'l' (abbreviation in sporting league tables) and 'l' is found in the answer.
'around' could be 'o' (a round letter) and 'o' is found within the answer.
an anagram of 'got' is 'tog' which is within the left over letters.
'island' could be 'is' (abbreviation) and 'is' is present in the answer.
A single letter 't' remains which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?