A tree with wavy sides caught protective headgear (4-3)

I believe the answer is:

wych-elm

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'a tree' is the definition.
(wych elm is a kind of tree)

'wavy sides caught protective headgear' is the wordplay.
'sides' means to remove the middle letters (only the letters on the sides are used).
'caught' becomes 'c' (cricket abbreviation).
'protective headgear' becomes 'helm' (I can't justify this - if you can you should believe this answer much more).
'wavy' with its centre taken out is 'wy'.
'wy'+'c'+'helm'='WYCH-ELM'

'with' is the link.

Can you help me to learn more?

(Other definitions for wych-elm that I've seen before include "Witch-hazel" , "European tree" .)

I've seen this clue in the Sydney Morning Herald.

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