The most common and most likely answer to this crossword clue is the 12 letter word ACCELERATION
I've seen this crossword clue in The Daily Telegraph
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Buddy explains!
The straight part
We know that "rate increase" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rate increase = acceleration.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ACCELERATION mean?
ACCELERATION noun- The act of accelerating, or the state of being accelerated; increase of motion or action; as opposed to retardation or deceleration.
- The amount by which a speed or velocity increases (and so a scalar quantity or a vector quantity).
- The change of velocity with respect to time (can include deceleration or changing direction).
- The advancement of students at a rate that places them ahead of where they would be in the regular school curriculum.