Relieved being let out without cap (5)
I believe the answer is:
eased
'relieved' is the definition.
(easing is a kind of relieving)
'let out without cap' is the wordplay.
'let out' becomes 'leased' (I've seen this before).
'without cap' means to remove the first letter.
'leased' with its initial letter removed is 'EASED'.
'being' acts as a link.
(Other definitions for eased that I've seen before include "Soothed - assuaged" , "Allievated" , "Lessened, pain or discomfort, say" , "Oiled" , "Given relief" .)