The most common and most likely answer to this crossword clue is the 3 plus 5 plus 5 letter word THE BLACK TOWER
T
H
E
B
L
A
C
K
T
O
W
E
R
Buddy explains!
The straight part
We know that "a P D James mystery" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a p d james mystery = the black tower.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.