Hypochondriac finally up to bed (3)
I believe the answer is:
cot
'bed' is the definition.
(cot is a kind of bed)
'hypochondriac finally up to' is the wordplay.
'finally' suggests the final letters.
'up' says the letters should be written backwards (in down clue: letters go upwards).
The final letter of 'hypochondriac' is 'c'.
'to' in reverse letter order is 'ot'.
'c'+'ot'='COT'
(Other definitions for cot that I've seen before include "Infant's bed" , "Folding bed - fingerstall" , "Baby bed" , "Small child's bed" , "Small bed with high sides" .)