Be rid of annoying new partner (5)
I believe the answer is:
bride
'new partner' is the definition.
'bride' can be an answer for 'partner'. I'm not sure about the 'new' bit.
'be rid of annoying' is the wordplay.
'of annoying' indicates anagramming the letters (I've seen 'annoying' mean this).
'be'+'rid'='berid'
'berid' with letters rearranged gives 'BRIDE'.
Can you help me to learn more?
(Other definitions for bride that I've seen before include "Groom's partner" , "The Woman In White, perhaps?" , "Newlywed" , "She's just about to be married" , "Woman getting wed" .)