The most common and most likely answer to this crossword clue is the 11 letter word INTERPOLATE
I've seen this crossword clue in The Times
I
N
T
E
R
P
O
L
A
T
E
More clues leading to the result INTERPOLATE
- Insert a note written by crime fighters
- Doctor writing to renegotiate role with patient
- Add one litre, tap turning
- Misleadingly, perhaps, put in policing organisation, getting knocked back
- Put in cross-border force at start of enquiry
- Enter intelligence agency with rum, tea
- Police force had put misleading words in
Buddy explains!

The straight part
We know that "Doctor writing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case doctor writing = interpolate.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 INTERPOLATE mean?
INTERPOLATE verb- To introduce (something) between other things; especially to insert (possibly spurious) words into a text.
- To estimate the value of a function between two points between which it is tabulated.
- During the course of processing some data, and in response to a directive in that data, to fetch data from a different source and process it in-line along with the original data.