Henry's coming in about rented house (6)
I believe the answer is:
chalet
'house' is the definition.
(I know that chalet is a type of house)
'henry's coming in about rented' is the wordplay.
'henry' becomes 'H' (symbol for the unit of electrical inductance).
'coming in' indicates putting letters inside.
'about' becomes 'ca' (abbreviation for 'circa').
'rented' becomes 'let' (I've seen this in another clue).
'h' inserted into 'ca' is 'cha'.
'cha'+'let'='CHALET'
(Other definitions for chalet that I've seen before include "The lac (anag.)" , "Swiss house with sloping roof and wide eaves" , "Swiss-style holiday house" , "wooden hut" , "Swiss summer hut" .)