Steaming in drink increased rapidly (4,2)
I believe the answer is:
shot up
'increased rapidly' is the definition.
(shoot up can mean to increase rapidly)
'steaming in drink' is the wordplay.
'steaming' becomes 'hot' (I've seen this in another clue).
'in' means one lot of letters goes inside another.
'drink' becomes 'sup' (to sup is to drink).
'hot' going inside 'sup' is 'SHOT UP'.
(Other definitions for shot up that I've seen before include "very quickly got high" , "Grew quickly" .)