Possible Clues:

• To 6 across is not to bury it, perhaps
• One does not dig deep to bury like this
• You don't have to go very deep to bury this, perhaps
• Personalize a bracelet
• Carve into the surface of
• Make an impression in French burial-place
• Carve into surface as of medal
• Chase what's serious - minor measure being given priority
• Avenger failing to impress
• To make an impression, use English with northern sort of accent