Leaf pest taking a rest under rose (3,6)

I believe the answer is:

red spider

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'leaf pest' is the definition.
'red spider' can be an answer for 'pest' (I have seen 'Little pest' mean 'red spider' so perhaps 'pest' could also mean 'red spider'). I am not certain of the 'leaf' bit.

'a rest under rose' is the wordplay.
'a rest' becomes 'spider' (I've seen this before).
'under' means one lot of letters go next to another (below, in a down clue).
'rose' becomes 'red' (shade of red).
'spider' after 'red' is 'RED SPIDER'.

'taking' acts as a link.

Can you help me to learn more?

(Other definitions for red spider that I've seen before include "Little pest" , "A mite" .)

I've seen this clue in The Times and The Sunday Times.

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