This time making a gear change in handling an important matter (10)
I believe the answer is:
addressing
'handling an important matter' is the definition.
'addressing' can be an answer for 'handling' ('address' can be a synonym of 'handle'). I am not sure about the 'an important matter' bit.
'this time making a gear change in' is the wordplay.
I cannot really understand how this works, but
'time' could be 'ad' (AD, Anno Domini, as opposed to BC, Before Christ) and 'ad' is located in the answer.
'gear' could be 'dress' (both can mean clothing) and 'dress' is found in the answer.
'in' is present in the answer.
A single letter 'g' remains which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for addressing that I've seen before include "job for 18 [ENVELOPE STUFFER]?" , "Speaking to" , "Flying activity" , "Dealing with" .)