Increase rapidly (7)
'increase rapidly' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for balloon that I've seen before include "Inflatable rubber bag, could be filled with hot air" , "Become inflated" , "In which Charlie Brown expressed himself" , "Brandy glass" , "Bag filled with gas or air" .)
'increase rapidly' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for escalate that I've seen before include "Increase in intensity or extent, like trouble brewing" , "mount in tension" , "Increase in extent or intensity (8)V" , "Magnify" , "Raise to higher level, perhaps war" .)