The most common and most likely answer to this crossword clue is the 13 letter word HOUSE-TRAINED
I've seen this crossword clue in Financial Times
H
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S
E
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More clues leading to the result HOUSE-TRAINED
Buddy explains!
The straight part
We know that "Going outside" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case going outside = house-trained.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 HOUSE-TRAINED mean?
HOUSE-TRAINED adjective- (of a pet) Trained not to excrete indoors.
- (by extension) Exhibiting behavior and habits that are consistent with good housekeeping.