Sadly bicker about who's first to give name for an Antarctic glacier (7)
I believe the answer is:
berwick
'name for an antarctic glacier' is the definition.
(Berwick Glacier in Antarctica)
'sadly bicker about who's first' is the wordplay.
'sadly' indicates an anagram.
'about' means one lot of letters goes inside another.
'who's first' becomes 'w' (1st letter of 'who').
'bicker' is an anagram of 'berick'.
'berick' enclosing 'w' is 'BERWICK'.
'to give' is the link.
(Other definitions for berwick that I've seen before include "Town on English-Scottish border, once neutral" , "- -upon-Tweed, town" .)