Amply recover after eruption of bile (9)

I believe the answer is:

liberally

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'amply' is the definition.
(thesaurus)

'recover after eruption of bile' is the wordplay.
I cannot quite understand how this works, but
'recover' could be 'rally' (rallying is a kind of recovering) and 'rally' is found within the answer.
an anagram of 'bile' is 'libe' which is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in The Independent.

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