People are getting on in this household (6)
I believe the answer is:
menage
'household' is the definition.
(I know that household can be written as menage)
'people are getting on in this' is the wordplay.
'people' becomes 'men' (men are people).
'are getting on' means one lot of letters go next to another.
'in this' becomes 'age' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'men'+'age'='MENAGE'
Can you help me to learn more?
(Other definitions for menage that I've seen before include "live together" , "A household, sometimes naughtily a trois" , "Members of a household" , "family group" , "a household, may be naughtily a trois" .)