Turning and pushing piece starts to annoy Magnus Carlsen terribly (3)
I believe the answer is:
cam
'turning and pushing piece' is the definition.
I can't judge whether this definition defines the answer.
'starts to annoy magnus carlsen terribly' is the wordplay.
'starts to' indicates taking the first letters.
'terribly' is an anagram indicator.
The first letters of 'annoy magnus carlsen' is 'amc'.
'amc' with letters rearranged gives 'CAM'.
Can you help me to learn more?
(Other definitions for cam that I've seen before include "River also called Granta" , "English river" , "Cambridge river" , "It controls the motion of engine cylinder valves" , "Tributary of the Ouse" .)