The most common and most likely answer to this crossword clue is the 4 letter word ELKS
I've seen this crossword clue in The Guardian
E
L
K
S
Buddy explains!

The straight part
We know that "Deer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deer = elks.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 ELKS mean?
ELKS noun- Any of various large species of deer such as the red deer, moose or wapiti (see usage notes).
- The European wild, whistling, or common swan (Cygnus cygnus, syn. Cygnus ferus).