The most common and most likely answer to this crossword clue is the 12 letter word TARAMASALATA
I've seen this crossword clue in The Guardian
T
A
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More clues leading to the result TARAMASALATA
- I'm going to eat starters of real authenticity: Indian spices for dip
- I'm leaving Indian dish — I’m grateful for fishy one
- I’m going to entertain artist with Indian spices for dip
- A curry in pie, a Greek dish
- A dip around the Aegean islands?
- Alma-Ata — a tsar upset on account of creamy food
- Athenian’s dip in defeat, alas, a marathon backfiring
- Ace curried mixture in pastry combined with a fish dish
Buddy explains!

The straight part
We know that "Athenian’s dip" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case athenian’s dip = taramasalata.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 TARAMASALATA mean?
TARAMASALATA noun- A Greek and Turkish dish of fish roe (carp or cod), lemon juice, breadcrumbs, onion, garlic, and olive oil; often served as a meze or with pitta bread