Flat in Glasgow initially used for part of the day (7)
I believe the answer is:
evening
'part of the day' is the definition.
(I've seen this before)
'flat in glasgow initially used' is the wordplay.
'flat' becomes 'even' (level).
'initially used' says to take the initial letters.
The initial letter of 'glasgow' is 'g'.
'even'+'in'+'g'='EVENING'
'for' is the link.
(Other definitions for evening that I've seen before include "Ironing" , "Latter part of the day" , "Levelling the score" , "late party" , "Late afternoon" .)