The most common and most likely answer to this crossword clue is the 12 letter word NAVEL-GAZING
I've seen this crossword clue in The Times
N
A
V
E
L
-
G
A
Z
I
N
G
Buddy explains!
The straight part
We know that "in self-contemplation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in self-contemplation = navel-gazing.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 NAVEL-GAZING mean?
NAVEL-GAZING verb- To engage in self-indulgent introspection.
- Contemplation of one's navel as an aid to meditation.
- Excessive focus on oneself; self-indulgent introspection.
- (sometimes derogatory) (Disproportionate) concentration on a single issue.