Cryptic crossword clue
Greedy — backing stratagem, that is — not heartless 8

The most common and most likely answer to this crossword clue is the 8 letter word ESURIENT

I've seen this crossword clue in The Times
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The straight part
We know that "Greedy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case greedy = esurient.
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 ESURIENT mean?

ESURIENT noun
  1. One who is greedy or hungry.
ESURIENT adjective
  1. Very greedy or hungry; ravenous; avid, eager.

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