The most common and most likely answer to this crossword clue is the 2 plus 4 plus 6 letter word MY DEAR WATSON
M
Y
D
E
A
R
W
A
T
S
O
N
Buddy explains!
The straight part
We know that "words addressed to doctor" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case words addressed to doctor = my dear watson.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.