Last month dons still sick — that's rough! (10)

'rough' is the definition.
(thesaurus)

'last month dons still sick' is the wordplay.
'last month' becomes 'ult' (short for 'last month' in correspondence).
'dons' indicates putting letters inside (don means to wear or put on).
'still sick' becomes 'uncured' (not yet cured).
'ult' put inside 'uncured' is 'UNCULTURED'.

'that's' is the link.