Dog endlessly pursuing evasive rodent (5)
I believe the answer is:
coypu
'rodent' is the definition.
(coypu is a kind of rodent)
'dog endlessly pursuing evasive' is the wordplay.
'dog' becomes 'pug' (pug is a kind of dog).
'endlessly' means to remove the last letter.
'pursuing' says to put letters next to each other.
'evasive' becomes 'coy' (coy can mean shy or evasive).
'pug' with its final letter removed is 'pu'.
'pu' after 'coy' is 'COYPU'.
(Other definitions for coypu that I've seen before include "S American rodent inadvertently introduced into Europe" , "Large semiaquatic rodent" , "South American beaver-like beast" , "Aquatic beaver-like rodent" , "Animal -- source of nutria fur" .)