At home with part covering piano examination (10)
I believe the answer is:
inspection
'examination' is the definition.
(inspection is a kind of examination)
'at home with part covering piano' is the wordplay.
'at home' becomes 'in' ('in' can be similar in meaning to 'at home').
'with' is a charade indicator (letters next to each other).
'part' becomes 'section' (sectioning is a kind of parting**).
'covering' indicates putting letters inside.
'piano' becomes 'p'.
'section' enclosing 'p' is 'spection'.
'in'+'spection'='INSPECTION'
(Other definitions for inspection that I've seen before include "perusal" , "Check" , "Close examination" , "Official examination" .)