Leave country singer regularly housed by English couple (8)
I believe the answer is:
emigrate
'leave country' is the definition.
(to emigrate is to leave one's country for another)
'singer regularly housed by english couple' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'housed by' indicates putting letters inside.
'english' becomes 'e' (abbreviation).
'couple' becomes 'mate' (synonyms).
The alternate letters of 'singer' are 'igr'.
'e'+'mate'='emate'
'igr' inserted within 'emate' is 'EMIGRATE'.
(Other definitions for emigrate that I've seen before include "Leave one's country to live elsewhere" , "Leave homeland" , "Leave home" , "Tiger Mae has gone abroad to live, oddly" , "Go to live and work in another country" .)