Lived out about half a mile in the country (5)
I believe the answer is:
wales
'the country' is the definition.
(country of the UK)
'lived out about half a mile' is the wordplay.
'lived out' becomes 'was' ('be' can be a synonym of 'live'. I am not sure about the 'out' bit.).
'about' is an insertion indicator.
'half a' suggests halving the letters.
'mile' with half the letters taken is 'le'.
'was' placed around 'le' is 'WALES'.
'in' is the link.
Can you help me to learn more?
(Other definitions for wales that I've seen before include "Land of Dai and Dylan" , "chooses" , "Home to Snowdonia and the Gower Peninsula" , "Its emblem is the leek" , "Principality, part of the UK" .)