Unease I’d picked up: I should participate in new quest (8)
I believe the answer is:
disquiet
'unease' is the definition.
(I know that unease can be written as disquiet)
'i'd picked up i should participate in new quest' is the wordplay.
'picked up' is a reversal indicator.
'should participate in' is an insertion indicator.
'new' indicates an anagram.
'id' back-to-front is 'di'.
'quest' anagrammed gives 'squet'.
'i' put into 'squet' is 'squiet'.
'di'+'squiet'='DISQUIET'
(Other definitions for disquiet that I've seen before include "concern" , "Restlessness" , "Mild anxiety" , "Feeling of unease" , "Vague unease, anxiety" .)