The most common and most likely answer to this crossword clue is the 7 letter word SLACKER
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More clues leading to the result SLACKER
Buddy explains!

The straight part
We know that "apathetic type" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case apathetic type = slacker.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 SLACKER mean?
SLACKER noun- One who procrastinates or is lazy.
- A person lacking a sense of direction in life; an underachiever.
- A person who seeks to avoid military service.
- A user of the Slackware Linux operating system.
- A member of a certain 1990s subculture associated with Generation X.