System encountered by daughter round house (6)
I believe the answer is:
method
'system' is the definition.
(thesaurus)
'encountered by daughter round house' is the wordplay.
'encountered' becomes 'met' ('meet' can be a synonym of 'encounter').
'by' says to put letters next to each other.
'daughter' becomes 'd'.
'round' means one lot of letters goes inside another.
'house' becomes 'ho' (abbreviation for house**).
'met'+'d'='metd'
'metd' enclosing 'ho' is 'METHOD'.
(Other definitions for method that I've seen before include "Procedure for achieving an end" , "'Means, way of achieving (6)'" , "Mode, procedure" , "Way of proceeding" , "System, perhaps even in madness" .)