The most common and most likely answer to this crossword clue is the 4 letter word HART
I've seen this crossword clue in Financial Times
H
A
R
T
More clues leading to the result HART
- Beater caught hunted creature
- Wild animal centre being spoken of
- Reportedly something that beats a mature male deer
- US lyricist’s courage mentioned
- Animal in river in Derby?
- Centre for the audience does attract one
- One panting for the psalmodist in the spirit of Spenser?
- Stag party is unending after taking heroin
- Stag partygoer’s ending in Panama, perhaps
- Animal showing courage having lost energy
Buddy explains!

The straight part
We know that "Stag" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stag = hart.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 HART mean?
HART noun- A male deer, especially the male of the red deer after his fifth year.
- A red deer or one of related species.
- A muscular organ that pumps blood through the body, traditionally thought to be the seat of emotion.
- Emotions, kindness, moral effort, or spirit in general.
- The seat of the affections or sensibilities, collectively or separately, as love, hate, joy, grief, courage, etc.; rarely, the seat of the understanding or will; usually in a good sense; personality.
- Courage; courageous purpose; spirit.
- Vigorous and efficient activity; power of fertile production; condition of the soil, whether good or bad.
- A term of affectionate or kindly and familiar address.
- Personality, disposition.
- A wight or being.
- A conventional shape or symbol used to represent the heart, love, or emotion: ♥ or sometimes <3.
- A playing card of the suit hearts featuring one or more heart-shaped symbols.
- The twenty-fourth Lenormand card.
- The centre, essence, or core.