The most common and most likely answer to this crossword clue is the 11 letter word MOLLYCODDLE
I've seen this crossword clue in The Daily Telegraph
M
O
L
L
Y
C
O
D
D
L
E
More clues leading to the result MOLLYCODDLE
Buddy explains!

The straight part
We know that "Pamper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pamper = mollycoddle.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 MOLLYCODDLE mean?
MOLLYCODDLE noun- A person, especially a man or a boy, who is pampered and overprotected.
- To be overprotective and indulgent toward; to pamper.