Cryptic crossword clue
Desirable mansion houses taxi base 10

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

I've seen this crossword clue in Financial Times
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The straight part
We know that "base" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case base = despicable.
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 DESPICABLE mean?

DESPICABLE noun
  1. A wretched or wicked person.
DESPICABLE adjective
  1. Fit or deserving to be despised; contemptible; mean

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