The most common and most likely answer to this crossword clue is the 8 letter word FIXATION
I've seen this crossword clue in The Daily Telegraph
F
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Buddy explains!

The straight part
We know that "Obsession" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obsession = fixation.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 FIXATION mean?
FIXATION noun- The act of fixing.
- The state of being fixed or fixated.
- The act of uniting chemically with a solid substance or in a solid form; reduction to a non-volatile condition; -- said of volatile elements.
- The act or process of ceasing to be fluid and becoming firm.
- In metals, a state of resistance to evaporation or volatilization by heat.
- A state of mind involving obsession with a particular person, idea or thing.
- Recording a creative work in a medium of expression for more than a transitory duration, thereby satisfying the "fixation" requirement for the purposes of copyright law.
- The change in a gene pool from a situation where there exists at least two variants of a particular gene (allele) to a situation where only one of the alleles remains.