Last in science, failing to pass (6)
I believe the answer is:
elapse
'pass' is the definition.
(I've seen this before)
'last in science failing' is the wordplay.
'last in' says to take the final letters.
'failing' becomes 'lapse' (I've seen this before).
The last letter of 'science' is 'e'.
'e'+'lapse'='ELAPSE'
'to' is the link.
(Other definitions for elapse that I've seen before include "Tick by" , "run by" , "Go by - pass away" , "Of time, pass by - please" , "Glide by" .)