Absence of nap, having start of afternoon off, is most curious (7)

I believe the answer is:

nosiest

I'm a little stuck... Click here to teach me more about this clue!

'most curious' is the definition.
('nosy' can be similar in meaning to 'curious')

I can't explain the remainder of the clue.

Can you help me to learn more?

(Other definitions for nosiest that I've seen before include "Most inquisitive" , "Most offensively curious" , "Most snoopy" , "One sits (anag)" , "Most prying" .)

I've seen this clue in The Telegraph.

Want a hint initially instead of a full solution? Install my app