Strongly urge (6)
(Other definitions for enjoin that I've seen before include "Prohibit by order" , "Command, instruct" , "Direct with authority" , "Order, tell" , "Instruct (to do a thing)" .)
'strongly urge' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for exhort that I've seen before include "Spur on" , "Entreat earnestly, urge" , "Strongly encourage (someone to action)" , "Encourage, urge" , "Strongly urge (someone to do something)" .)