Husband picked up reference book lacking top cover (7)

I believe the answer is:

hatless

'lacking top cover' is the definition.
(without a hat on top of one's head)

I cannot understand how the rest of the clue works.

(Other definitions for hatless that I've seen before include "Uncovered" , "Without a titfer" .)

I've seen this clue in The Guardian.

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