Tick whatever's left of school exams carelessly (3)
I believe the answer is:
sec
'tick' is the definition.
(I've seen this in another clue)
'left of school exams carelessly' is the wordplay.
'left of' says to take the initial letters (the leftmost letter in the word).
The first letters of 'school exams carelessly' is 'SEC'.
'whatever's' is the link.
I am not very happy about this link. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for sec that I've seen before include "period not lasting long" , "sort of function" , "Twinkling" , "Dry, like wine" , "Religious group." .)