Somewhere on your contract documentation you may be able to find information regarding when they are prepared to upgrade you, or you could call them or check your account online.
As a rule of thumb, most suppliers are prepared to upgrade within the contract period and this is often 6 months prior. So for an 18 month contract they will upgrade after 12 months and for a 24 month contract they will upgrade after 18 months. You are unlikely to receive an upgrade of handset just 12 months into a 24 month contract. This can be a nuisance if the handset has a problem with a 12 month warranty during a 24 month contract if the warrenty has expired.
However, as Juliefrazz says, they often add the remaining period onto the end of the contract.
As TSA says, you can threaten to take your business elsewhere but phone providers take a variety of factors into consideration when dealing with disconnections and retentions and low users don't make them a lot of money. That said, inside the contract period, you aren't really in a strong position to make such a threat.