Greek primate's eaten shellfish (5)
I believe the answer is:
gaper
'eaten shellfish' is the definition.
The definition suggests a singular noun which matches the answer.
'greek primate's' is the wordplay.
'greek' becomes 'g' (philological abbreviation).
'primate's' becomes 'aper' (I can't explain this - if you can you should give a lot more credence to this answer).
'g'+'aper'='GAPER'
Can you help me to learn more?
(Other definitions for gaper that I've seen before include "Fish; burrowing mollusc" , "one staring in wonder" , "one visibly amazed" , "who yawns?" , "Anglerfish" .)