Mistake in LA, including African party in backing group (3,4)
I believe the answer is:
fan club
'backing group' is the definition.
(group which backs a person or thing)
'mistake in la including african party' is the wordplay.
'mistake in la' becomes 'flub' (I can't explain this - if you can you should give a lot more credence to this answer).
'including' means one lot of letters goes inside another.
'african party' becomes 'anc' (African National Congress, South African party).
'flub' placed around 'anc' is 'FAN CLUB'.
'in' is the link.
Can you help me to learn more?
(Other definitions for fan club that I've seen before include "Fervent admirers" , "Association of devotees" , "Admiring band" , "Association of ardent followers" , "Devoted followers collectively" .)