A flower the last of four to improve (5)
I believe the answer is:
rhone
'a flower' is the definition.
(River Rhone, something which flows)
'last of four to improve' is the wordplay.
'last of' suggests the final letters.
'to improve' becomes 'hone' (honing is a kind of improving).
The final letter of 'four' is 'r'.
'r'+'hone'='RHONE'
'the' is the link.
(Other definitions for rhone that I've seen before include "River flowing from Alps to the French Med" , "Fr. river and wine" , "French flower" , "River at Avignon and Arles" , "River rising in Switzerland and flowing into the Mediterranean" .)