Boosting output current of mosfet Driver IC
In your Previous Question, you show a schematic with your existing gate drive circut with a 30 ohm resistor in series with the gate driver output.   



Using 15 volt gate drive and 30 ohms, your gate drive turn off current is limited to  15v/30 = 0.5 amps (initially). 

You can speed up the turn off by adding a diode D2.  Whether this will give you the turn off you desire, could be tested before you consider other circuitry. The additional diode does not effect the turn on (reverse biased during turn on).  The diode bypasses the 30 ohm gate resistor during turnoff. This is a common practice for achieving higher turn off current.  

Reducing your 30 ohm to 10 ohms would also improve turn on current.  



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The TC4420 driver chip  you ask about could be used to increase drive output (and sink). You will likely need more bypass (storage) capacitor to accommodate the increased peak current.  You should still use the diode to improve turn off current.