‘give rise to’ means ‘to cause something’ in the Cambridge dictionary. But I think ‘arise’ is more similar to ‘cause’ than ‘rise’ according to this.
What is difference between ‘give rise to’ and ‘cause’? And why ‘rise’ not ‘arise’?
The word rise, in this context, is a noun meaning beginning or origin, whereas arise is a verb which means to begin to occur or to exist.
So give rise to means to cause the beginning of something, e.g. The general's success gave rise to new problems.
If you want to use arise instead you could write it as The general's success made new problems arise.