As a tenant you are responsible for arranging your own contents insurance. Buildings insurance is the responsibility of the landlord, but anything that you own inside the property is your own responsibility to insure.
A standard contents insurance policy will not usually cover those who are renting. Instead there is tenants insurance which is designed to specifically cover rental properties and tenants possessions.
If your property comes already furnished it is advisable to check with the landlord what items are already covered by the landlords insurance. Any uninsured items should be added to your insurance as if any items become damaged it is likely to be the tenant’s responsibility to replace the item or pay for the damage out of their security deposit.