The most common and most likely answer to this crossword clue is the 8 letter word DREDGING
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More clues leading to the result DREDGING
Buddy explains!

The straight part
We know that "Digging up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case digging up = dredging.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does DREDGING mean?
DREDGING verb- To make a channel deeper or wider using a dredge.
- To bring something to the surface with a dredge.
- (Usually with up) to unearth.
- To sprinkle (food) with spices or seasonings, using a dredge.
- That which is dredged up.
- The act of using a dredger or excavator to dredge a harbour, river, channel or watercourse.