Cryptic crossword clue
Elected Tory chap round Rugby not compatible 11

The most common and most likely answer to this crossword clue is the 11 letter word INCONGRUENT

I've seen this crossword clue in The Times
I
N
C
O
N
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T

Buddy explains!

The straight part
We know that "not compatible" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not compatible = incongruent.
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 INCONGRUENT mean?

INCONGRUENT adjective
  1. Out of place, incompatible, inharmonious, not congruent
  2. Of or relating to two numbers that have different remainders when divided by a third number

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