The most common and most likely answer to this crossword clue is the 4 plus 11 letter word BIRD SANCTUARIES
I've seen this crossword clue in The Guardian
B
I
R
D
S
A
N
C
T
U
A
R
I
E
S
Buddy explains!
The straight part
We know that "nests that should be protected" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nests that should be protected = bird sanctuaries.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.