I have a little problem here, this week I'm starting a new D&D next adventure using the ongoing Basic Rules, I'm planning on buy the PHB next month and PC already asked me if they can change their classes in the middle of the adventure so their party has more variations to the starter 4 party.
Any ideas on how I can do this? or its better to re-start with the new rules?
Don't restart unless you want to.
There are two clear options for this, and it's completely up to your preference (the current rules provide no clear guidance on this)
Simply allow them to change PCs. Write their old PC out and their new PC in. Bring the new PC in at the current level and if everyone else has a magic item, it might not hurt to let them pick one out (the current rules for higher level PCs involve no awarding of magic items, or more than basic cash, I expect fuller rules on this in the PHB).
Write in a class change for the PC. This might provide you with more story potential for you and your players. Work with your players to write a story where their character changes classes. Perhaps the cleric decides to go Paladin or the Wizard is struck with sudden inspiration and becomes a Bard.
The final option, and one I'm not including above because we know little of the mechanics and what the requirements would be (and as such we don't know if your PCs would even qualify), would be to let them multiclass. In this case they'd take levels of their other class and gain some of their low level abilities. Again, we don't know all the details of the 5e multiclass system, but we do know it involves level based MC like non-4th editions.
With whatever you decide to do, keep in mind that this is your collective story that you're all telling. Keep good communication between yourself and your players. If they want to play different characters, find a way to weave it into your story. There isn't a need to start over, unless you want to, that's totally kosher too. But don't feel like you have to start over simply because your players have decided they want to try out the fancy new classes that drop with the PHB.
Wax Eagle's answer ("Simply allow them to change PCs" and "Write in a class change for the PC") cover what I see as two of the three options. The last one came up with some regularity when I was running the playtest: let the player rebuild the character and declare that of course Quill has always been a Barbarian. Some people don't like retcons, but my own experience is that people move on pretty quickly. It lets you keep inter-PC relationships that have built up and doesn't interrupt ongoing story lines with a special "Why Bob changed classes" story. My own playtest game is now converting to the basic rules and we'll be doing some of this now, as our poor druid's class no longer exists and at least one of our fighter's build paths disappeared.
Just have them remake their character as a new class, keeping their treasure and XP. This is normally not permitted by the rules (and multi classing, which will certainly be added in the Players Handbook, won't cover a replacement of class), but in this case there's no reason not to use your power as DM to override the rules.
Think of the Starter Set like a pilot episode of a new series: sometimes, characters completely change, are played by different actors, or disappear entirely between the pilot and the first episode. That lack of continuity will be felt, but it will fade after a few sessions with the new characters.
Simply have them pick up a cursed item that changes their class and swaps their existing stats around to reflect the new class. They keep all their stuff, level etc. Or have a higher power do it, or an insane guy uses his last wish to cause the switch - whatever doesn't piss off the entire group. You may also want to impose a penalty such as an experience loss so the rest of the group doesn't think this is something they can do whenever they want.
