Rapid increase in anti-termination allowance (13)

I believe the answer is:

proliferation

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'rapid increase' is the definition.
'proliferation' can be an answer for 'increase' (I've seen this before). I'm unsure of the 'rapid' bit.

'anti-termination allowance' is the wordplay.
'anti termination' becomes 'prolife' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'allowance' becomes 'ration' (I've seen this before).
'prolife'+'ration'='PROLIFERATION'

'in' is the link.

Can you help me to learn more?

(Other definitions for proliferation that I've seen before include "Increase in numbers" , "Increase (of nuclear weapons)" .)

I've seen this clue in The Daily Express.

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