Jack's companion is missing Jack badly (3)
I believe the answer is:
ill
'badly' is the definition.
('ill' can be adverbial as in 'ill-advised')
'jack's companion is missing jack' is the wordplay.
'jack's companion' becomes 'jill' (I've seen this before).
'is missing' indicates named letters should be taken away.
'jack' becomes 'J' (playing card abbreviation).
'jill' with 'j' taken away is 'ILL'.
(Other definitions for ill that I've seen before include "Where to find Chicago" , "Hardly - sick" , "Under the weather" , "Not well, sick" , "Harm" .)