Crossword Genius

Trappings of office I gain unexpectedly after getting elected head of school (8)

Ross

I believe the answer is:

insignia

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

'trappings of office' is the definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.

'i gain unexpectedly after getting elected head of school' is the wordplay.
'unexpectedly' indicates an anagram.
'after getting' says to put letters next to each other.
'elected' becomes 'in'.
'head of' suggests taking the first letters.
The initial letter of 'school' is 's'.
'gain' anagrammed gives 'gnia'.
'i'+'gnia'='ignia'
'in'+'s'='ins'
'ignia' put after 'ins' is 'INSIGNIA'.

Can you help me to learn more?

(Other definitions for insignia that I've seen before include "Badge of membership" , "arms" , "Emblems of rank" , "military mark" , "Stars and stripes, say" .)

I've seen this clue in The Telegraph.
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