Doctor and old lady taking part in tiresome process (9)
I believe the answer is:
rigmarole
'tiresome process' is the definition.
'rigmarole' can be an answer for 'process' (rigmarole is a kind of process). I am unsure of the 'tiresome' bit.
'doctor and old lady taking part in' is the wordplay.
'doctor' becomes 'rig' (I've seen this before).
'and' says to put letters next to each other.
'old lady' becomes 'ma'.
'taking part in' becomes 'role' (I can't explain this - if you can you should give a lot more credence to this answer).
'rig'+'ma'+'role'='RIGMAROLE'
Can you help me to learn more?
(Other definitions for rigmarole that I've seen before include "Long, complex stuff" , "Palaver" , "Nonsensical procedure" , "Tedious procedure" , "Complex procedure" .)