Moved along cave and dislodged diamonds (8)
I believe the answer is:
advanced
'moved along' is the definition.
'cave and dislodged diamonds' is the wordplay.
'dislodged' indicates an anagram.
'diamonds' becomes 'd' (abbreviation in bridge say).
'cave'+'and'='caveand'
'caveand' is an anagram of 'advance'.
'advance'+'d'='ADVANCED'
(Other definitions for advanced that I've seen before include "subbed" , "progressive" , "promoted" , "At a higher level" , "Far ahead in development or progress" .)