Crossword Genius

Had one’s fill — following Indian way in English coastal town (7)

Ross

I believe the answer is:

margate

I'm a little stuck... Click here to teach me more about this clue!

'town' is the definition.

'had one's fill following indian way in english coastal' is the wordplay.
I cannot really see how this works, but
'had' could be 'ate' (e.g. I had an ice cream) and 'ate' is found within the answer.
'one' could be 'a' and 'a' is found within the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for margate that I've seen before include "N. Kent seaside resort" , "resort town" , "which people may visit for seaside holiday" , "place in England" , "coastal resort" .)

I've seen this clue in The Hindu.
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