The most common and most likely answer to this crossword clue is the 7 letter word HANG-UP
I've seen this crossword clue in The Guardian
H
A
N
G
-
U
P
More clues leading to the result HANG-UP
- Emotional problem to end conversation abruptly
- Complex way to end a call
- Emotional problem causing Chinese dog to get upset
- How to finish phone call becomes an obsession
- . Unforeseen obstacle leading to shortfall of labourer at Gulf state
- Gun shot during accident causes difficulty
- Obsession to finish call
- Complex way to end communication?
Buddy explains!

The straight part
We know that "Obsession/finish call" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obsession/finish call = hang-up.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.
Crossword Answer definitions
HANG-UP noun- An emotional difficulty or a psychological inhibition; a complex.
- An unforeseen obstacle to progress; a hitch.