Crossword Genius

Discharge former prince deposing country’s leader (10)

Ross

I believe the answer is:

exhalation

'discharge' is the definition.
(thesaurus)

'former prince deposing country's leader' is the wordplay.
I cannot quite understand how this works, but
'former' could be 'ex' (prefix meaning former or onetime) and 'ex' is located in the answer.
'prince' could be 'hal' (I've seen this before) and 'hal' is found within the answer.
This explanation may well be incorrect...

(Another definition for exhalation that I've seen is " Breathing out".)

I've seen this clue in The Times.
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