Slick lie yielding students a sneaky day off (6)
I believe the answer is:
sickie
'a sneaky day off' is the definition.
'slick lie yielding students' is the wordplay.
'yielding' is a deletion indicator.
'students' becomes 'll'.
'slick'+'lie'='slicklie'
'slicklie' with 'll' removed is 'SICKIE'.
(Other definitions for sickie that I've seen before include "Leave taken with feigned illness" , "In day off work" , "ill-deserved leave?" , "Day off for malingerer" .)