Starts to slyly yawn and drop off at meeting (5)
I believe the answer is:
synod
'meeting' is the definition.
(type of religious meeting)
'starts to slyly yawn and drop off' is the wordplay.
'starts to' indicates taking the first letters.
'and' says to put letters next to each other.
'drop off' becomes 'nod' (I've seen this before).
The first letters of 'slyly yawn' is 'sy'.
'sy'+'nod'='SYNOD'
'at' is the link.
(Other definitions for synod that I've seen before include "Assembly of the clergy" , "Ecclesiastical gathering" , "Clerical assembly" , "Forum for discussing" , "Ecclesiastical assembly" .)