The most common and most likely answer to this crossword clue is the 8 letter word HEDONISM
I've seen this crossword clue in The Daily Telegraph
H
E
D
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M
More clues leading to the result HEDONISM
- Hard way to admit transgression after rebuffing indulgence
- Is getting married after wild hen do the height of indulgence?
- Supply me with dosh in search for pleasure
- Search for fun the don is misrepresenting? Not entirely
- A university teacher is introduced to cannabis largely as pleasure-seeking
- Sensuality‘s odd methods in wasting time
- Pleasure-seeking housewife disheartened — academic is married!
- Explosive fellow is male seeking excessive pleasure
- What’s embraced by the don is mindless pursuit of pleasure
- Gratification of ‘The Don’ is murder
Buddy explains!

The straight part
We know that "Pleasure-seeking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pleasure-seeking = hedonism.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 HEDONISM mean?
HEDONISM noun- The belief that pleasure or happiness is the highest good in life. Some hedonists, such as the Epicureans, have insisted that pleasure of the entire mind, not just pleasure of the senses, is the highest good.
- A general devotion to the pursuit of pleasure.