Dictator's person vetting design of squares (7)

I believe the answer is:

chequer

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

'design of squares' is the definition.
'chequer' can be an answer for 'design' (I've seen this before). I'm not certain of the 'of squares' bit.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for chequer that I've seen before include "Divide into alternately coloured squares" , "design" , "Mark into squares of different colours" , "last man on board" , "Alternation of colours" .)

I've seen this clue in The Times.

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