Dad went inside, nothing left but his October birthstone (4)
I believe the answer is:
opal
'october birthstone' is the definition.
(I've seen this in another clue)
'dad went inside nothing left but his' is the wordplay.
I cannot really see how this works, but
'dad' could be 'pa' (both can mean one's father) and 'pa' is located in the answer.
'nothing' could be 'o' (looks like zero - 0) and 'o' is located in the answer.
'left' could be 'l' (common abbreviation) and 'l' is found within the answer.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for opal that I've seen before include "Type of gemstone" , "Gem stone" , "National gemstone of Australia" , "Form of hydrated silica, often used as a gemstone" , "Milky-white mineral" .)