Crab's beginning to be overwhelmed by long right claw (6)
I believe the answer is:
pincer
'claw' is the definition.
(I know that claw can be written as pincer)
'crab's beginning to be overwhelmed by long right' is the wordplay.
'beginning to' indicates taking the first letters.
'be overwhelmed by' means one lot of letters goes inside another (inserted letters get absorbed or overwhelmed).
'long' becomes 'pine' (to pine for someone is to long for them).
'right' becomes 'r' (common abbreviation).
The initial letter of 'crabs' is 'c'.
'c' going inside 'pine' is 'pince'.
'pince'+'r'='PINCER'
(Other definitions for pincer that I've seen before include "Crab's claw" , "Grasping limb of a crustacean" , "Claw, nipper" , "This movement is a converging attack" , "Surrounding (movement)" .)