The most common and most likely answer to this crossword clue is the 11 letter word INATTENTIVE
I
N
A
T
T
E
N
T
I
V
E
More clues leading to the result INATTENTIVE
Buddy explains!

The straight part
We know that "Oblivious" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case oblivious = inattentive.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 INATTENTIVE mean?
INATTENTIVE adjective- Of or pertaining to lack of attention; not paying attention; careless.