The most common and most likely answer to this crossword clue is the 11 letter word UNCONCERNED
U
N
C
O
N
C
E
R
N
E
D
Buddy explains!

The straight part
We know that "indifferent" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case indifferent = unconcerned.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 UNCONCERNED mean?
UNCONCERNED adjective- Indifferent and having no interest; aloof.
- Not worried, anxious or apprehensive.
- Having no involvement.