Living without Jack, I found, is capital (7)
I believe the answer is:
beijing
'is capital' is the definition.
(capital of China)
'living without jack i' is the wordplay.
'living' becomes 'being' ('be' can be a synonym of 'live').
'without' indicates putting letters inside ('without' can be similar in meaning to 'outside').
'jack' becomes 'J' (playing card abbreviation).
'j'+'i'='ji'
'being' enclosing 'ji' is 'BEIJING'.
'found' is the link.
(Other definitions for beijing that I've seen before include "(Eastern) capital" , "Eastern city" , "Gin jibe in China" , "2008 Olympics host" , "Chinese capital" .)