Formal examination of private possessions! (3,10)

I believe the answer is:

kit inspection

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

'of private possessions' is the definition.
The definition suggests a singular noun which matches the answer.

'formal examination' is the wordplay.
I cannot quite see how this works, but
'examination' could be 'inspection' (synonyms) and 'inspection' is located in the answer.
The remaining letters 'kit' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in The Irish News.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.