Most convenient direction around? That's south (7)
I believe the answer is:
easiest
'most convenient' is the definition.
(I've seen this before)
'direction around? that's south' is the wordplay.
'direction' becomes 'east' (compass direction).
'around?' indicates putting letters inside.
'that's' becomes 'ie'.
'south' becomes 'S' (abbreviation).
'ie'+'s'='ies'
'east' enclosing 'ies' is 'EASIEST'.
(Other definitions for easiest that I've seen before include "Least hard" , "Requiring the least amount of effort" , "most amenable" , "Most convenient" , "Posing least difficulty" .)