The most common and most likely answer to this crossword clue is the 8 letter word BABUSHKA
I've seen this crossword clue in The Guardian
B
A
B
U
S
H
K
A
More clues leading to the result BABUSHKA
- Old Russian’s British alias taking in US president
- 1980 pop song, sung to grandmother
- British alias assumed by Kate’s foreign granny
- Degree given to ex-president Ford’s granny in Moscow
- Granny made beastly remark about president and king
- Old woman‘s wild after graduate regularly larks about
- Graduate takes public transport to Hong Kong wearing a scarf
- Old woman's headscarf
- Grandmother's scarf
- Elderly Russian‘s bleat about President Kennedy initially
Buddy explains!

The straight part
We know that "grandmother" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case grandmother = babushka.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 BABUSHKA mean?
BABUSHKA noun- An old woman.
- A woman’s headscarf, tied under the chin.
- Russian doll, matryoshka