Article one put out after a bill for a rate increase (12)
I believe the answer is:
acceleration
'rate increase' is the definition.
'acceleration' can be an answer for 'increase' (I have seen 'Increase of speed' mean 'acceleration' so perhaps 'increase' could also mean 'acceleration'). I am not sure about the 'rate' bit.
'article one put out after a bill' is the wordplay.
'put out' indicates anagramming the letters.
'after' says to put letters next to each other.
'a bill' becomes 'ac' (abbreviation for account).
'article'+'one'='articleone'
'articleone' with letters rearranged gives 'celeration'.
'celeration' put after 'ac' is 'ACCELERATION'.
'for a' is the link.
Can you help me to learn more?
(Other definitions for acceleration that I've seen before include "The increasing of speed" , "Speeding-up" , "Speeding up" , "Rate of increase of speed" .)