Country dwelling with animal enclosure outside over the top (7)
I believe the answer is:
cottage
'country dwelling' is the definition.
(rural residence)
'animal enclosure outside over the top' is the wordplay.
'animal enclosure' becomes 'cage' (I've seen this in another clue).
'outside' indicates putting letters inside.
'over the top' becomes 'OTT' (abbreviation).
'cage' going around 'ott' is 'COTTAGE'.
'with' acts as a link.
(Other definitions for cottage that I've seen before include "Small home" , "Rural dwelling" , "Small one-storied house" , "building" , "Cheese pie industries all may chase this" .)