Not burning to be incorporated into new text (7)
I believe the answer is:
extinct
'not burning' is the definition.
(eg an extinct volcano)
'incorporated into new text' is the wordplay.
'incorporated' becomes 'inc'.
'into' means one lot of letters goes inside another.
'new' indicates an anagram.
'text' with letters rearranged gives 'extt'.
'inc' inserted into 'extt' is 'EXTINCT'.
'to be' is the link.
(Other definitions for extinct that I've seen before include "gone forever" , "gone for ever" , "Of volcano, no longer active" , "Having died out, like the dinosaur" , "No longer existing" .)