Minor damage from fire one’s left to go out (5)
I believe the answer is:
singe
'minor damage from fire' is the definition.
I can't judge whether this defines the answer.
'one's left to go out' is the wordplay.
'one' becomes 'single' (synonyms).
'left' becomes 'l' (common abbreviation).
'to go out' indicates named letters should be taken away.
'single' with 'l' taken away is 'SINGE'.
Can you help me to learn more?
(Other definitions for singe that I've seen before include "Superficial burn" , "Result of match accident" , "Scorch lightly" , "slight burn" , "Sear" .)