Carla ordered politician something illuminating (3,4)

I believe the answer is:

arc lamp

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'something illuminating' is the definition.
I can't tell whether this definition defines the answer.

'carla ordered politician' is the wordplay.
'ordered' is an anagram indicator.
'politician' becomes 'MP' (Member of Parliament).
'carla' is an anagram of 'arcla'.
'arcla'+'mp'='ARC-LAMP'

Can you help me to learn more?

(Other definitions for arc lamp that I've seen before include "Source of bright light" , "one of the bright lights" , "Intense illuminator" , "Electric light source" .)

I've seen this clue in The Daily Express.

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