The most common and most likely answer to this crossword clue is the 7 letter word STEARIN
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Buddy explains!

The straight part
We know that "A constituent of tallow" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a constituent of tallow = stearin.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 STEARIN mean?
STEARIN noun- Solid fat.
- The triglyceride of stearic acid.