The most common and most likely answer to this crossword clue is the 15 letter word PARSNIP/STACHYS
P
A
R
S
N
I
P
/
S
T
A
C
H
Y
S
Buddy explains!
The straight part
We know that "veg/labiate plant" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case veg/labiate plant = parsnip/stachys.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.