"I will EXchange my car with a new one as soon as I get some money." "Change" is used when there is no replacement mentioned in the sentence. i.e. "I changed the lightbulb." "Exchange" is used when the replacement is mentioned. i.e. "I exchanged the blue dress for a red one." I think "with" and "for" can be used interchangeably, ("I exchanged my car with/for a new one"), but I think I hear "for" more often.

You only need to change "with" with "for" I will change my car for a new one as soon as I get some money.

I understand what you're saying, but I would use a different verb. "Change" seems like you're trading or switching with someone else. I would use "buy" and "sell". "I will buy a new car as soon as I get some money." Then, if someone asks what you will do with the car you have now, you can say that you will sell it.