Relative being at home upset teacher periodically (5)
I believe the answer is:
niece
'relative' is the definition.
(type of relative)
'at home upset teacher periodically' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'upset' is a reversal indicator.
'periodically' indicates alternate letters (letters must be selected 'every so often').
The alternating letters of 'teacher' are 'ece'.
'in' written backwards gives 'ni'.
'ni'+'ece'='NIECE'
'being' acts as a link.
(Other definitions for niece that I've seen before include "Criminal" , "member of different generation" , "[PRIEST'S] daughter?" , "A sibling's child" , "Daughter of a sibling" .)