In recession, LA rents rise rapidly (6)
I believe the answer is:
spiral
'rise rapidly' is the definition.
(rise in a spiral pattern)
'in recession la rents' is the wordplay.
'in recession' says the letters should be written backwards (letters recede or go back).
'rents' becomes 'rips' ('rip' can be a synonym of 'rent').
'la'+'rips'='larips'
'larips' backwards is 'SPIRAL'.
(Other definitions for spiral that I've seen before include "Ever widening curve" , "Shape of coil or helix" , "Helical curve" , "Scandalise" , "Type of staircase" .)