When should I tell my current job that I’m leaving?

I got offered a new job that would start mid-July. I’m a psychotherapist and I want to give my clients time to process saying goodbye, etc. However I want to stay at my job for at least another 6 weeks so I can keep getting pay and benefits. When should I tell my current employer that I’m leaving? I’m worried that if I tell them too soon they would let me go before I want to leave. But I also feel like telling them sooner rather than later provides more time for closure and finishing up my work tasks in a leisurely manner.

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