The most common and most likely answer to this crossword clue is the 3 letter word DIG
I've seen this crossword clue in The Times
D
I
G
More clues leading to the result DIG
- Like an archaeological excavation
- Appreciate archaeologists’ undertaking
- Like indigenous houses
- Understand excavation
- Falling over, soldier died — make his grave?
- Appreciate having to enquire more closely
- Taunt US swot, bilingual, lot neglected
- Understand Government papers should be returned
- Figure lacking sex appeal produces this taunt
- Enjoy what archaeologists do
Buddy explains!

The straight part
We know that "make his grave" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make his grave = dig.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 DIG mean?
DIG noun- An archeological or paleontological investigation, or the site where such an investigation is taking place.
- A plodding and laborious student.
- A thrust; a poke.
- A tool for digging.
- A defensive pass of the ball that has been attacked by the opposing team.
- A cutting, sarcastic remark.
- A rare or interesting vinyl record bought second-hand.
- To move hard-packed earth out of the way, especially downward to make a hole with a shovel. Or to drill, or the like, through rocks, roads, or the like. More generally, to make any similar hole by moving material out of the way.
- To get by digging; to take from the ground; often with up.
- To take ore from its bed, in distinction from making excavations in search of ore.
- To work like a digger; to study ploddingly and laboriously.
- To investigate, to research, often followed by out or up.
- To thrust; to poke.
- To defend against an attack hit by the opposing team by successfully passing the ball
- To understand or show interest in.
- To appreciate, or like.
- Digoxin.