Moving cautiously, say, to admit a transgression (6)
I believe the answer is:
easing
'moving cautiously' is the definition.
'easing' can be an answer for 'moving' (easing is a kind of moving). I'm not sure about the 'cautiously' bit.
'say to admit a transgression' is the wordplay.
'say' becomes 'eg' (both can mean for example).
'to admit' indicates putting letters inside.
'transgression' becomes 'sin' (sin is a kind of transgression).
'a'+'sin'='asin'
'eg' going around 'asin' is 'EASING'.
Can you help me to learn more?
(Other definitions for easing that I've seen before include "Allaying, alleviating" , "Moderation - relief" , "falling off?" , "Making lighter" , "Becoming less severe" .)