Rise while courts start and finish (6)
I believe the answer is:
ascend
'rise' is the definition.
(I know that rise can be written as ascend)
'while courts start and finish' is the wordplay.
'while' becomes 'as' (eg 'while I walked' means 'as I walked').
'start' says to take the initial letters.
'and' says to put letters next to each other.
'finish' becomes 'end' (come to an end).
The initial letter of 'courts' is 'c'.
'as'+'c'+'end'='ASCEND'
(Other definitions for ascend that I've seen before include "Soar" , "Gain height" , "rise in status" , "Mount" , "Move upward" .)