I’ll rest, maybe, with the lattice screen (7)

I believe the answer is:

trellis

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'lattice screen' is the definition.
'trellis' can be an answer for 'screen' (thesaurus). I'm not sure about the 'lattice' bit.

'i'll rest maybe' is the wordplay.
'maybe' is an anagram indicator.
'ill'+'rest'='illrest'
'illrest' anagrammed gives 'TRELLIS'.

'with the' acts as a link.

Can you help me to learn more?

(Other definitions for trellis that I've seen before include "Rose clambers over this" , "latticework in the garden" , "climbers train on it" , "Lattice structure" , "Garden climber support" .)

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

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