Service from graduate isn't fantastic (6)
I believe the answer is:
Here is my best explanation:
'service' is the definition.
'graduate isn't fantastic' is the subsidiary indication.
'graduate' becomes 'ma' (**).
'fantastic' indicates anagramming the letters.
'isnt' with letters rearranged gives 'tins'.
'from' is the link.
(Other definitions for matins that I've seen before include "Church service", "Morning service", "Morning prayers or bird-songs", "Isn't ma given to morning prayers?", "Anglican morning service", "church service" and "C of E's daily morning service".)