The most common and most likely answer to this crossword clue is the 10 letter word INVETERATE
I've seen this crossword clue in The Sunday Telegraph
I
N
V
E
T
E
R
A
T
E
More clues leading to the result INVETERATE
- Confirmed spineless creature lacks courage and fibre essentially
- One event to be rescheduled before charge is confirmed
- Confirmed version of trainee vet
- Confirmed international tariff will include new event
- Angry about rescheduled event being confirmed
- Variety of native tree that’s deep-rooted
- Old cut in middle of winter could be chronic
- Habitual attire even when running
Buddy explains!

The straight part
We know that "deep-rooted" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deep-rooted = inveterate.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 INVETERATE mean?
INVETERATE verb- To fix and settle after a long time; to entrench.
- Firmly established from having been around for a long time; of long standing
- (of a person) Having had a habit for a long time
- Malignant; virulent; spiteful.