Nasty predator may show little sign of grief (8)
I believe the answer is:
teardrop
'little sign of grief' is the definition.
(tears may be cried in grief)
'nasty predator' is the wordplay.
'nasty' is an anagram indicator.
'predator' is an anagram of 'TEARDROP'.
'may show' is the link.
(Other definitions for teardrop that I've seen before include "Globule of moisture indicating distress" , "A single globule of eye moisture" , "Secretion from lachrymal gland" , "It comes from the lachrymal gland" , "Bit of salty moisture" .)