The most common and most likely answer to this crossword clue is the 6 letter word SHADOW
I've seen this crossword clue in The Times
S
H
A
D
O
W
More clues leading to the result SHADOW
- Closely follow play, having to put in notice
- Follow poster used in display
- Closely follow pig, tricked to go inside
- Dog kept cutting inside pig
- Follow famous Irish playwright around party
- Follow notice, hugged by escort
- Doctor who's bad with old x-ray: do ring practice!
- . Performance about publicity trail
- Dog Bill’s entered into competition
- Dog straying — how sad
Buddy explains!

The straight part
We know that "Dog" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dog = shadow.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 SHADOW mean?
SHADOW noun- A dark image projected onto a surface where light (or other radiation) is blocked by the shade of an object.
- Relative darkness, especially as caused by the interruption of light; gloom, obscurity.
- A area protected by an obstacle (likened to an object blocking out sunlight).
- A reflected image, as in a mirror or in water.
- That which looms as though a shadow.
- A small degree; a shade.
- An imperfect and faint representation.
- (police) A trainee, assigned to work with an experienced officer.
- One who secretly or furtively follows another.
- An inseparable companion.
- A drop shadow effect applied to lettering in word processors etc.
- An influence, especially a pervasive or a negative one.
- A spirit; a ghost; a shade.
- (Latinism) An uninvited guest accompanying one who was invited.
- In Jungian psychology, an unconscious aspect of the personality.
- To shade, cloud or darken.
- To block light or radio transmission from.
- To secretly or discreetly track or follow another, to keep under surveillance.
- To represent faintly and imperfectly.
- To hide; to conceal.
- To accompany (a professional) during the working day, so as to learn about an occupation one intends to take up.
- To make (an identifier, usually a variable) inaccessible by declaring another of the same name within the scope of the first.
- To apply the shadowing process to (the contents of ROM).
- Unofficial, informal, unauthorized, but acting as though it were.
- Having power or influence, but not widely known or recognized.
- Acting in a leadership role before being formally recognized.
- Part of, or related to, the opposition in government.