The most common and most likely answer to this crossword clue is the 4 plus 4 letter word KNEE DEEP
K
N
E
E
D
E
E
P
Buddy explains!
The straight part
We know that "Thoroughly involved with" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case thoroughly involved with = knee deep.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 KNEE DEEP mean?
KNEE DEEP adjective- Reaching up to the knees.
- Submerged to the knees.
- (by extension) Deeply involved in something, or preoccupied with something.