Its heavenly under a tree! (7)

I believe the answer is:

sublime

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

'its heavenly' is the definition.
I can't judge whether this definition defines the answer.

'under a tree' is the wordplay.
'under' becomes 'sub' (I've seen this before).
'a tree' becomes 'lime' (type of tree).
'sub'+'lime'='SUBLIME'

Can you help me to learn more?

(Other definitions for sublime that I've seen before include "Transcendent" , "Exalted; awesome" , "Glorious; supreme" , "Heavenly" , "Magnificent" .)

I've seen this clue in The Irish News.

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