Heave up out of wells, possibly (5)

I believe the answer is:

swell

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

'heave up' is the definition.
'swell' can be an answer for 'heave' (thesaurus). I'm unsure of the 'up' bit.

'wells possibly' is the wordplay.
'possibly' indicates anagramming the letters.
'wells' is an anagram of 'SWELL'.

'out of' acts as a link.

Can you help me to learn more?

(Other definitions for swell that I've seen before include "Excellent (slang)" , "VIP?" , "mushroom" , "Inflate - fine" , "Enlarge; excellent" .)

I've seen this clue in the Evening Standard.

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