The most common and most likely answer to this crossword clue is the 7 letter word PEDICLE
I've seen this crossword clue in The Times
P
E
D
I
C
L
E
Buddy explains!

The straight part
We know that "Stalk" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stalk = pedicle.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 PEDICLE mean?
PEDICLE noun- A fleshy line used to attach and anchor brachiopods and some bivalve molluscs to a substrate.
- The attachment point for antlers in cervids.
- A stalk that attaches a tumour to normal tissue
- Pedicel (any sense)
- Peduncle (any sense)
- Part of a skin or tissue graft temporarily left attached to its original site.
- A fetter for the foot.