Progressive increase of delight about regular social appearances (10)
I believe the answer is:
escalation
'progressive increase' is the definition.
'escalation' can be an answer for 'increase' (escalation is a kind of increase). I'm not certain of the 'progressive' bit.
'delight about regular social appearances' is the wordplay.
'delight' becomes 'elation' (I've seen this before).
'about' means one lot of letters goes inside another.
'regular social appearances' becomes 'sca' (I can't justify this - if you can you should give a lot more credence to this answer).
'elation' going around 'sca' is 'ESCALATION'.
'of' acts as a link.
Can you help me to learn more?
(Other definitions for escalation that I've seen before include "sudden rise" , "Rapid rise in level" , "expansion" , "Rapid growth" .)