Turned up tailing shy rodent (5)
I believe the answer is:
coypu
'rodent' is the definition.
(coypu is a kind of rodent)
'turned up tailing shy' is the wordplay.
'turned' is a reversal indicator.
'tailing' is a charade indicator (letters next to each other) (to tail can mean to go after or follow).
'shy' becomes 'coy' (coy can mean shy or modest).
'up' back-to-front is 'pu'.
'pu' put after 'coy' is 'COYPU'.
(Other definitions for coypu that I've seen before include "Large South American aquatic rodent" , "Creature in fur coat" , "Large South American beaver-like rodent" , "S American rodent inadvertently introduced into Europe" , "Beaver-like creature" .)