Crossword Genius

Be prolific for half an hour in a jazz-band (6)

Ross

I believe the answer is:

abound

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

'be prolific' is the definition.
(I've seen this before)

'half an hour in a jazz-band' is the wordplay.
'half an hour' becomes 'ou' (I am not sure about this - if you are sure you should believe this answer much more).
'in' means one lot of letters goes inside another.
'a jazz' is an anagram indicator (letters in an improvised order).
'band' is an anagram of 'abnd'.
'ou' inserted inside 'abnd' is 'ABOUND'.

'for' is the link.

Can you help me to learn more?

(Other definitions for abound that I've seen before include "Be plentiful, say fish in river" , "Be widely available" , "Be in plentiful supply" , "Swell" , "Be plentiful, be present on great quantities" .)

I've seen this clue in the Evening Standard.
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