A trainer doesn't need it to keep in good shape! (4-4)

I believe the answer is:
shoe-tree
'good shape' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.
'a trainer doesn't need it to keep in' is the wordplay.
'a trainer' becomes 'shoe' (I've seen this before).
'doesn't need' becomes 'tre' (I can't justify this - if you can you should give a lot more credence to this answer).
'it' becomes 'e' ('e' can mean 'electronic' which is similar to 'IT').
'to keep in' means one lot of letters goes inside another.
'tre' placed around 'e' is 'tree'.
'shoe'+'tree'='SHOE-TREE'
Can you help me to learn more?
I've seen this clue in the Evening Standard.
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