Dear me, it's becoming a bore (8)
I believe the answer is:
diameter
'a bore' is the definition.
(thesaurus)
'dear me it's becoming' is the wordplay.
'becoming' indicates anagramming the letters.
'dear'+'me'+'it'='dearmeit'
'dearmeit' is an anagram of 'DIAMETER'.
(Other definitions for diameter that I've seen before include "Straight line drawn through centre of circle (8)" , "Circle's width" , "Longest line in a circle" , "A demerit for line bisecting a circle" , "Two radii" .)