Gathering involving fool and English doctor, extremely lively (8)
I believe the answer is:
assembly
'gathering' is the definition.
(I know that gathering can be written as assembly)
'fool and english doctor extremely lively' is the wordplay.
'fool' becomes 'ass' (both can mean a stupid person).
'and' says to put letters next to each other.
'english' becomes 'e' (abbreviation).
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'extremely' suggests removing the centre (only the extremes of the word are used).
'lively' with its centre removed is 'ly'.
'ass'+'e'+'mb'+'ly'='ASSEMBLY'
'involving' is the link.
(Other definitions for assembly that I've seen before include "start of day at school" , "Gathering, congretation 98)" , "synod" , "School morning gathering" , "Legislative gathering" .)