Climbing part of tree-lined Aventine to make escape (5)
I believe the answer is:
evade
'escape' is the definition.
(evading is a kind of escaping)
'climbing part of tree-lined aventine' is the wordplay.
'climbing' is a reversal indicator (in a down clue, letters climb up).
'part of' says the answer is hidden in the clue.
'edave' is hidden in the letters of 'tree lined aventine'.
'edave' in reverse letter order is 'EVADE'.
'to make' acts as a link.
(Other definitions for evade that I've seen before include "Dodge by cleverness or trickery" , "Dodge - prevaricate" , "bypass" , "Circumvent, dodge" , "Dodge or escape" .)