Serious enough to make one late (5)
I believe the answer is:
fatal
'serious' is the definition.
(thesaurus)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for fatal that I've seen before include "Unavoidable" , "making one late" , "critical" , "Pernicious" , "Resulting in disaster or death" .)