Lived on border with diamonds (7)
I believe the answer is:
resided
'lived' is the definition.
(residing is a kind of living)
'on border with diamonds' is the wordplay.
'on' becomes 're' ('on' can be mean 'with reference to').
'border' becomes 'side' (I've seen this in other clues).
'with' says to put letters next to each other.
'diamonds' becomes 'd' (abbreviation in bridge say).
're'+'side'+'d'='RESIDED'
(Other definitions for resided that I've seen before include "stayed" , "Abode" , "Sojourned" , "Settled" , "Dwelt" .)