Up to tree rocks taper off (5,3)
I believe the answer is:
peter out
'taper off' is the definition.
(synonyms)
'up to tree rocks' is the wordplay.
'rocks' indicates an anagram.
'up'+'to'+'tree'='uptotree'
'uptotree' is an anagram of 'PETER OUT'.
(Other definitions for peter out that I've seen before include "End gradually" , "Decrease gradually before ending" , "Diminish feebly" , "'Run down, taper off (5,3)'" , "Dwindle away to nothing" .)