Speak vehemently of former demand (7)

I believe the answer is:

exclaim

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'speak vehemently' is the definition.
'exclaim' can be an answer for 'speak' (thesaurus). I'm unsure of the 'vehemently' bit.

'former demand' is the wordplay.
'former' becomes 'ex' (prefix meaning former or onetime).
'demand' becomes 'claim' (claim is a kind of demand).
'ex'+'claim'='EXCLAIM'

'of' acts as a link.

Can you help me to learn more?

(Other definitions for exclaim that I've seen before include "Speak suddenly" , "Cry out suddenly, as from pain or surprise" , "Call" , "Shout out" , "Express surprise" .)

I've seen this clue in The Irish Independent.

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