The most common and most likely answer to this crossword clue is the 6 letter word FETISH
I've seen this crossword clue in The Times
F
E
T
I
S
H
More clues leading to the result FETISH
- Search to capture alien life? It’s an obsession
- Fixation with France and French — want to be guillotined!
- Female alien is hot; a thing that gets you going!
- Peculiar interest, this, strangely requiring iron initially
- Angle covering alien’s obsession
- Place turning up in extremely foolish fixation
- Undertaking is hard but not a thing to get excited about
- On vacation enjoyment is restricted by what may be sole obsession
- This cryptic obsession
- Thief’s developed obsession
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 = fetish.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 FETISH mean?
FETISH noun- Something which is believed to possess, contain, or cause spiritual or magical powers; an amulet or a talisman.
- Sexual attraction to or arousal at something sexual or nonsexual, such as an object or a part of the body.
- An irrational, or abnormal fixation or preoccupation; an obsession.