Mother’s period home given to daughter, very bright person! (10)
I believe the answer is:
mastermind
'very bright person' is the definition.
(a very clever person)
'mother's period home given to daughter' is the wordplay.
'mother's' becomes 'ma's' (Ma is another word for mother or mum).
'period' becomes 'term' (term is a kind of period).
'home' becomes 'in' ('he's home' can mean 'he's in').
'given to' is a charade indicator (letters next to each other).
'daughter' becomes 'd' (genealogical abbreviation).
'mas'+'term'+'in'+'d'='MASTERMIND'
(Other definitions for mastermind that I've seen before include "Ringleader" , "Planning supremo" , "Intellectual" , "Person with outstanding intellect" , "Criminal genius" .)