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 definition defines the answer.
'one's left to go out' is the wordplay.
'one' becomes 'single' (synonyms).
'left' becomes 'l' (common abbreviation).
'to go out' is a deletion indicator.
'single' with 'l' removed 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" .)