Thoughtless person put stuff to be burnt here? (7)
I believe the answer is:
ingrate
'thoughtless person' is the definition.
(ungrateful person)
'stuff to be burnt here?' is the wordplay.
I cannot really see how this works, but
'be' could be 'rate' (rating is a kind of being) and 'rate' is found within the answer.
This may be the basis of the clue (or it may be nonsense).
'put' is the link.
(Other definitions for ingrate that I've seen before include "Thankless type" , "Unthankful person" , "Unappreciative type" , "No thanks, I say!" , "Tangier (anag)" .)