The most common and most likely answer to this crossword clue is the 7 letter word ANNATES
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The straight part
We know that "First fruits" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case first fruits = annates.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 ANNATES mean?
ANNATES noun- The first year's profits of a Catholic benefice, as traditionally paid directly to the Pope.
- The half-year's stipend payable for the vacant half-year after the death of a parish minister, to which his family or nearest of kin have right under an act of 1672.