English proceed initially to Split for self-inflating experience (3,4)
I believe the answer is:
ego trip
'english proceed initially to split' is the definition.
I can't tell whether this definition defines the answer.
'self-inflating experience' is the wordplay.
I cannot quite see how this works, but
'self' could be 'ego' (synonyms) and 'ego' is found within the answer.
'experience' could be 'trip' (I have seen 'Hallucinatory experience' mean 'trip' so perhaps 'experience' could also mean 'trip') and 'trip' is found within the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'for' acts as a link.
Can you help me to learn more?
(Other definitions for ego trip that I've seen before include "Self-glorification episode" , "Bout of boosting self-esteem" , "Vainglorious course of action" , "Self-gratifying experience" , "Experience enjoyed by the conceited" .)