Moving slowly and carefully, taking ages in movement (6)
I believe the answer is:
easing
'moving' is the definition.
(easing is a kind of moving)
'ages in movement' is the wordplay.
'movement' indicates an anagram (letters move around).
'ages'+'in'='agesin'
'agesin' with letters rearranged gives 'EASING'.
'slowly and carefully taking' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for easing that I've seen before include "giving assistance" , "Moderation - relief" , "relaxing" , "Making lighter" , "Relieving tension" .)