At home with nurse? That's mean! (6)
I believe the answer is:
intend
'mean' is the definition.
(to intend to something is to mean it)
'at home with nurse?' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'with' means one lot of letters go next to another.
'nurse?' becomes 'tend' (tend can mean to nurse or look after).
'in'+'tend'='INTEND'
'that's' is the link.
(Other definitions for intend that I've seen before include "Purport" , "1 dn [DESIGN]" , "Signify" , "Plan, propose" , "Have as purpose or resolve" .)