Exclusive group’s simple dwelling overlooking great lake (7)
I believe the answer is:
coterie
'exclusive group's' is the definition.
(I've seen this in another clue)
'simple dwelling overlooking great lake' is the wordplay.
'simple dwelling' becomes 'cot' (cot can mean a simple cottage).
'overlooking' means one lot of letters go next to another (in a down clue, some letters go above others).
'great lake' becomes 'erie' (Erie is one of the Great Lakes).
'cot'+'erie'='COTERIE'
(Other definitions for coterie that I've seen before include "Small exclusive group of people" , "Exclusive social circle" , "Exclusive circle of people with common purpose" , "Select group" , "Small exclusive circle with a common purpose" .)