Rise is mostly used for things or persons that move from a lower to a higher lever, go up: the sun rises every morning. The plane rose to 2000 metres. All rise! (a call for people in a court of law to stand). Dracula has risen from the dead! (came back to life). He rose to fame (became famous). Note that raise is a transitive verb that corresponds to the intransitive rise: something rises (by itself), but we raise something (we cause it to rise): The students raised their hands. Are they going to raise our salaries?
Arise is used to speak of situations that (usually unexpectedly) come up. So, problems, matters, needs, opportunities etc. arise: Could you stay over for a couple of hours should the need arise?