The most common and most likely answer to this crossword clue is the 8 letter word ANCESTOR
I've seen this crossword clue in Financial Times
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More clues leading to the result ANCESTOR
- Forebear requires an exotic escort
- Old family member losing head jigs on peak
- Forebear caught stabbing a wise old king
- One's predecessor reacts on being corrected
- Participator in your descent or ascent, oddly
- One’s predecessor reacts on being condemned
- Relative acceleration with new model Escort
- Dipping into finances to repay grandpa?
- Escort an eccentric old relative
- An odd escort for an older person
Buddy explains!

The straight part
We know that "great-grandma" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case great-grandma = ancestor.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 ANCESTOR mean?
ANCESTOR noun- One from whom a person is descended, whether on the father's or mother's side, at any distance of time; a progenitor; a forefather.
- An earlier type; a progenitor
- One from whom an estate has descended;—the correlative of heir.
- One who had the same role or function in former times.
- A word or phrase which serves as the origin of a term in another language.
- To be an ancestor of.