The most common and most likely answer to this crossword clue is the 7 letter word DIGGING
I've seen this crossword clue in The Daily Telegraph
D
I
G
G
I
N
G
Buddy explains!
The straight part
We know that "Enjoying a bit of archaeology" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case enjoying a bit of archaeology = digging.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 DIGGING mean?
DIGGING verb- 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.
- The action performed by a person or thing that digs.
- A place where ore is dug, especially certain localities in California, Australia, etc. where gold is obtained.
- Region; locality