Progress from practice finally, after unrehearsed act (7)
I believe the answer is:
improve
'progress' is the definition.
(thesaurus)
'practice finally after unrehearsed act' is the wordplay.
'finally' suggests the final letters.
'after' says to put letters next to each other.
'unrehearsed act' becomes 'improv'.
The last letter of 'practice' is 'e'.
'e' after 'improv' is 'IMPROVE'.
'from' acts as a link.
(Other definitions for improve that I've seen before include "Train" , "Make better in quality" , "Polish" , "Enhance" , "Get or make better" .)