Blessed with a word of greeting one day in the middle of the week (8)
I believe the answer is:
hallowed
'blessed' is the definition.
('hallow' can be a synonym of 'bless')
'a word of greeting one day in the middle of the week' is the subsidiary indication.
'a word of greeting one' becomes 'halle' (I am not sure about this - if you are sure you should believe this answer much more).
'day' becomes 'd'.
'in the middle' means one lot of letters goes inside another.
'of' becomes 'o'.
'the week' becomes 'w' (abbreviation).
'halle'+'d'='halled'
'o'+'w'='ow'
'halled' enclosing 'ow' is 'hallowed'.
'with' is the link.
(Other definitions for hallowed that I've seen before include "Consecrated, holy" , "Revered" , "Made holy and honoured" , "Sanctified" , "Held holy" .)