At home with half-sister in Bury (5)
I believe the answer is:
inter
'bury' is the definition.
(to inter is to put into the ground)
'at home with half-sister' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'with' means one lot of letters go next to another.
'half' means to take half the letters.
'sister' with half the letters taken is 'ter'.
'in'+'ter'='INTER'
'in' acts as a link.
(Other definitions for inter that I've seen before include "foreign team" , "Put underground" , "Cover" , "Bury - Milan football club" , "Put under the earth" .)