The most common and most likely answer to this crossword clue is the 7 letter word TICKLER
I've seen this crossword clue in Financial Times
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More clues leading to the result TICKLER
Buddy explains!

The straight part
We know that "Delicate problem/someone who’ll please" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case delicate problem/someone who’ll please = tickler.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 TICKLER mean?
TICKLER noun- One who tickles.
- A person who or thing which amuses or excites.
- A reminder.
- A latex condom that has additional protrusions, for enhancing the sexual pleasure of the user.
- Something puzzling or difficult; a conundrum.
- A tickler file, file cabinet, or similar containing memoranda of deadlines arranged in date order.
- A prong used by coopers to extract bungs from casks.
- A dram of spirits.