Protection in bed? That's old hat (6)
I believe the answer is:
cloche
I believe this clue is a double definition.
'protection in bed?' is the first definition.
(a cloche might protect a flower bed)
'old hat' is the second definition.
(old-fashioned type of hat)
'that's' acts as a link.
(Other definitions for cloche that I've seen before include "Woman's helmet-like hat" , "Protective covering for plants from frost" , "Transparent cover for forcing plants" , "protection for young stock?" , "Hat; cover for plants" .)