I received a partial payment back on my tax refund, When should I expect the rest to come through?

If your refund was adjusted the IRS will send you a letter explaining why. 

How much is missing?  Federal and state come separately.  Were you having the fees deducted from your refund?

A common adjustment is if you claimed the Recovery rebate credit on 1040 line 30 when you already got the Stimulus payment or got the second one after you filed or reported the wrong amounts or entered them in the wrong box.  Do you have an amount on line 30?

TT is not notified when the IRS adjusts or offsets your tax refund.