Tender name, possibly showing affection (10)
I believe the answer is:
endearment
'affection' is the definition.
(I've seen this before)
'tender name possibly' is the wordplay.
'possibly' is an anagram indicator.
'tender'+'name'='tendername'
'tendername' anagrammed gives 'ENDEARMENT'.
'showing' acts as a link.
(Other definitions for endearment that I've seen before include "sign of affection" , "Fondness" , "Affectionate term" , "Pet name" , "Love, maybe" .)