Beseech members to finish off first course after tea starts (7)
I believe the answer is:
entreat
'beseech' is the definition.
(I know that beseech can be written as entreat)
'course after tea starts' is the wordplay.
'course' becomes 'entre' (I can't justify this - if you can you should give a lot more credence to this answer).
'starts' says to take the initial letters.
The first letters of 'after tea' is 'at'.
'entre'+'at'='ENTREAT'
'members to finish off first' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for entreat that I've seen before include "Beg earnestly, beseech" , "Beg earnestly, plead with" , "Ask (someone) earnestly" , "Pray" , "Will's pass" .)