The most common and most likely answer to this crossword clue is the 8 letter word INDULGES
I've seen this crossword clue in The Guardian
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More clues leading to the result INDULGES
Buddy explains!

The straight part
We know that "Pampers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pampers = indulges.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 INDULGES mean?
INDULGES verb- (often followed by "in"): To yield to a temptation or desire.
- To satisfy the wishes or whims of.
- To give way to (a habit or temptation); not to oppose or restrain.
- To grant an extension to the deadline of a payment.
- To grant as by favour; to bestow in concession, or in compliance with a wish or request.