Alarm after game's first shooter (6)

I believe the answer is:

gunman

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'shooter' is the definition.
(I know that shooter can be written as gunman)

'alarm after game's first' is the wordplay.
'alarm' becomes 'unman' (I can't explain this - if you can you should believe this answer much more).
'after' is a charade indicator (letters next to each other).
'game's first' becomes 'g' (ust letter of 'game').
'unman' after 'g' is 'GUNMAN'.

Can you help me to learn more?

(Other definitions for gunman that I've seen before include "As killer" , "Sean O'Casey play 'Shadow of a . . . . . .'" , "Armed person" , "Eg, sniper" , "Armed criminal" .)

I've seen this clue in The Telegraph.

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