Held by mate, the right tie (6)
I believe the answer is:
tether
'tie' is the definition.
(I know this)
'held by mate the right' is the wordplay.
'held by' indicates a hidden word.
'TETHER' is hidden in the letters of 'mate the right'.
(Other definitions for tether that I've seen before include "Tie animal to prevent from straying" , "Rope to fasten grazing animal" , "Tie up with a rope, an animal perhaps" , "Bond" , "Rope keeping animal from straying" .)