In the direction of first of the old hospital areas (7)
I believe the answer is:
towards
'in the direction of' is the definition.
(I've seen this before)
'first of the old hospital areas' is the wordplay.
'first of the' becomes 't' (1st letter of 'the').
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'hospital areas' becomes 'wards' (I've seen this in another clue).
't'+'o'+'wards'='TOWARDS'
(Other definitions for towards that I've seen before include "In the direction of" , "Getting near" , "Regarding" , "it's not coming away" , "approaching" .)