Crossword Genius

Very smelly soldiers beginning to exasperate His Maj? (7)

Ross

I believe the answer is:

reeking

I'm a little stuck... Click here to teach me more about this clue!

'very smelly' is the definition.
'reeking' can be an answer for 'smelly' (thesaurus). I'm unsure of the 'very' bit.

'soldiers beginning to exasperate his maj?' is the wordplay.
I cannot quite understand how this works, but
'soldiers' could be 're' (Royal Engineers) and 're' is found within the answer.
The remaining letters 'eking' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for reeking that I've seen before include "Stinking" , "Foul smelling" , "With a very unpleasant smell" , "Emitting smoke" , "Having a foul smell" .)

I've seen this clue in The Independent.
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