Service still good around middle of morning (8)
I believe the answer is:
evensong
'service' is the definition.
(type of church service)
'still good around middle of morning' is the wordplay.
'still' becomes 'even' (synonyms).
'good around middle of morning' becomes 'song' (I can't explain this - if you can you should believe this answer much more).
'even'+'song'='EVENSONG'
(Other definitions for evensong that I've seen before include "Service of evening prayer in Church of England" , "... Prayers" , "Anglican service" , "Vespers" , "Late afternoon church service" .)