Your question can be answered only after knowing the terms of the contract. Furthermore, you have not mentioned the legal status of your organization (Firm, Company, Proprietorship, Shop, etc.).
Inform Your Employer
In any case, it is better to inform your employer about the new job and get relieved. Take a relieving letter from them. If you are working as a Cashier and leave without informing them, the management, if really nasty, could file a false complaint of misappropriation of cash. Generally, professional companies do not file such false cases, but how professional the management is, only you can determine.