Cryptic crossword clue
Politician tending to arouse lecherous thoughts, by agreement 10

The most common and most likely answer to this crossword clue is the 10 letter word CONSENSUAL

I've seen this crossword clue in The Times
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The straight part
We know that "by agreement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case by agreement = consensual.
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 CONSENSUAL mean?

CONSENSUAL adjective
  1. With permission, with consensus, without coercion; allowed without objecting or resisting
  2. Existing, or made, by the mutual consent of two or more parties
  3. Excited or caused by sensation, sympathy, or reflex action, and not by conscious volition

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