Crossword Genius

Independent person in house, cheeky type

Ross

I believe the answer is:

imp

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'house cheeky type' is the definition.
Although both the answer and definition are singular nouns, I don't understand how one could define the other.

'independent person' is the wordplay.
'independent' becomes 'i'.
'person' becomes 'mp' (MP is an example).
'i'+'mp'='IMP'

'in' acts as a link.

Can you help me to learn more?

(Other definitions for imp that I've seen before include "Evil spirit" , "Scamp" , "pickle" , "little chap" , "old-fashioned graft" .)

I've seen this clue in The Daily Mail.
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