Getting better? Yours truly’s demonstrating that (9)
I believe the answer is:
improving
'getting better?' is the definition.
(getting better is a kind of improving)
'yours truly's demonstrating that' is the wordplay.
I cannot quite see how this works, but
'demonstrating' could be 'proving' (proving is a kind of demonstrating) and 'proving' is located in the answer.
'yours truly's' could be 'im' (I'm) and 'im' is located in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for improving that I've seen before include "Recovering" , "Getting better" , "Making better" .)