The most common and most likely answer to this crossword clue is the 6 letter word PANDER
I've seen this crossword clue in Independent
P
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More clues leading to the result PANDER
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The straight part
We know that "Minister to the passions" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case minister to the passions = pander.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 PANDER mean?
PANDER noun- A person who furthers the illicit love-affairs of others; a pimp or procurer.
- An offer of illicit sex with a third party.
- An illicit or illegal offer, usually to tempt.
- (by extension) One who ministers to the evil designs and passions of another.
- To tempt with, to appeal or cater to (improper motivations, etc.); to assist in gratification.
- To offer illicit sex with a third party; to pimp.
- To act as a pander for (somebody).