Hi Manav,
The electric field outside a conductor carrying varying current will be non-zero.
The explanation is :
The Interal charges and external charges in a condcutor carrying current organize themselves such that electirc field inside the conductor is always zero. But there remains a net external charge on the conductor due to varying current. This will Induce an electric field outside the condcutor. There are no charges present in an area outside conductor which can balance the electric field due to charges in the conductor. Thus there will exist a field outside condcutor.
You can also apply Gauss law to calculate the electric field outside the conductor. It will come proportionate to the charge inside the conductor due to current.
Please feel free to ask as many questions as you have.
Puneet