Crossword Genius

The French graduate outside public house near hotel all overcome in general? (8)

Ross

I believe the answer is:

hannibal

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

'general?' is the definition.
(I've seen this before)

'the french graduate outside public house near hotel all overcome' is the wordplay.
I cannot quite understand how this works, but
'graduate' could be 'ba' (someone with a Bachelor of Arts degree) and 'ba' is found in the answer.
'house' could be 'h' and 'h' is found in the answer.
This may be the basis of the clue (or it may be nonsense).

'in' acts as a link.

Can you help me to learn more?

(Other definitions for hannibal that I've seen before include "Famous general who crossed the Alps with elephants and defeated the Romans" , "Carthaginian general, d.182 BC" , "Great Carthaginian general who led army over the Alps against Rome" , "Carthaginian general who crossed the Alps to defeat Rome" , "Carthaginian general who fought Rome" .)

I've seen this clue in The Irish Times.
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