Depending on how long you have collected.
Once your claim is established, you have a 52 weeks period to collect for example 40 (depending on your area's unemployment rate and how long you worked before) weeks of benefits.
So after your contract is completed, you could renew your old claim, if it is still within the 52 weeks period and claim the remaining weeks of entitlement, if not all the 40 weeks were claimed.
If you new contract job has a higher salary, you may choose to establish a new claim to receive higher weekly benefit.