Love to break quickly into a modern industry (9)
I believe the answer is:
aerospace
'a modern industry' is the definition.
(modern business or industry)
'love to break quickly' is the wordplay.
'love' becomes 'eros' (Greek god of love).
'to break' indicates putting letters inside (inserted letters break into the word).
'quickly' becomes 'apace' (synonyms).
'eros' placed into 'apace' is 'AEROSPACE'.
'into' acts as a link.
(Other definitions for aerospace that I've seen before include "rocket industry" , "zone near Earth" , "Technology of planes, rockets, etc" , "Nasa's speciality" , "The aviation world" .)