Fasten twice, oddly (3)
I believe the answer is:
tie
'fasten' is the definition.
(tying is a kind of fastening)
'twice oddly' is the wordplay.
'oddly' indicates alternate letters.
The alternating letters of 'twice' are 'TIE'.
(Other definitions for tie that I've seen before include "Failure to win" , "line above notes" , "Draw; link" , "hamper" , "Encumbrance" .)