King backed an extremely wicked activity (7)
I believe the answer is:
knavery
'wicked activity' is the definition.
'knavery' can be an answer for 'activity' (knavery is a kind of activity). I'm not certain of the 'wicked' bit.
'king backed an extremely' is the wordplay.
'king' becomes 'K' (abbreviation for king in chess).
'backed' says the letters should be written in reverse.
'extremely' becomes 'very' (very can mean extremely or considerably).
'an' reversed gives 'na'.
'k'+'na'+'very'='KNAVERY'
Can you help me to learn more?
(Other definitions for knavery that I've seen before include "Rascally behaviour" , "Wickedness" , "Chicanery" , "Deceitful behaviour" , "fraud" .)