A question we often get asked is "will my phone work if I switch telco?".
The good news is that the answer should be a big Yes, but it comes to who sold you the phone and how you bought it.
1. A phone bought on a contract
If you've bought a phone on a contract in most cases, the answer should be yes. When you get a smartphone when you sign a contract, its unlocked, which means you can pop in any other SIM card and use it on any other Australian or overseas network. If for some reason a phone you bought on a contract is locked to a network (which probably also means your phone is very old), your telco will unlock it free of charge.
2. A phone bought outright
If you've bought your phone outright, the answer is also yes. This is only fair considering that you have paid upfront and in full for the phone, you should be able to do anything you like with it. And you can.
3. A phone bought with a Prepaid SIM
If you've got your phone as part of a prepaid deal, there's a chance you might have to pay an unlocking fee, depending on how long you've had it for. Telcos subsidise the price of prepaid phones, and as such, lock them to their network. If you've had the phone for over six-months though, most telcos will unlock it for free (although Telstra still charges a small fee).
4. A phone bought online from overseas (grey imports)
If you bought your phone overseas or through a grey importer such as Kogan or Dick Smith (where they're a local retailer who sells overseas stock), the phone will be sold unlocked, but you need to double-check that the model you are buying supports all network frequencies in Australia. Some manufacturers sell slightly different variations of a phone in different markets, potentially with different frequency support.
For example, the OnePlus 3, a popular affordable smartphone that isn't available in Australia but that can be imported, doesn't support 700Mhz, a frequency used for 4G by both Telstra and Optus. You'll still get 4G connectivity on the OnePlus 3, but you might find yourself getting kicked back to 3G in areas where the only 4G is delivered by 700Mhz.
If a phone doesn't support a specific frequency, you'll still get network connectivity, it might just not be quite as reliable. This does however depend on where you live, and what frequencies the networks near you are built using.