Time, that is, to fasten (3)
I believe the answer is:
tie
'fasten' is the definition.
(I know that fasten is a kind of attach)
'time that is' is the wordplay.
'time' becomes 't' (abbreviation).
'that is' becomes 'ie' (short for Latin 'id est', 'that is').
't'+'ie'='TIE'
'to' acts as a link.
(Other definitions for tie that I've seen before include "Attach, fasten" , "Fasten, link to" , "Get even" , "Accessory" , "Bind with a cord" .)