The most common and most likely answer to this crossword clue is the 4 letter word IBEX
I've seen this crossword clue in The Times
I
B
E
X
More clues leading to the result IBEX
- Beast that is cross — bull initially confined
- One reportedly burns tough goat
- I live with cross mountain dweller
- I live with cross Alpine climber
- Mountain goat from heart of Tibet, and last of lynx
- Regularly liable, finally tax high liver
- Goat from central Tibet – spot marked thus
- Wild goat having to live caged in square
- Regularly nibbled by goat
- Mounted team that collects live goats
Buddy explains!

The straight part
We know that "tough goat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tough goat = ibex.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 IBEX mean?
IBEX noun- A type of wild mountain goat of the genus Capra, such as the species Capra ibex.