Timelines can be unpredictable and the possibility of a deal falling through hangs in the air. If you're a 'fly by the seat of your pants' type, then by all means, give it a shot. However, generally the safest option is to wait until your existing property has sold, get a realistic sense of how much budget you have to buy a new house and make decisions from there.
There are a few reasons why this more cautious approach is recommended. First of all, depending on how your previous property was sold you may not know what your budget will be moving forward. Waiting until the sale is finalised means your next purchase will be made with a realistic budget in mind and the possibilities of overcommitment avoided. There are also the complexities of selling one property whilst buying another simultaneously to be considered. Both the selling and buying of property are considered among the most stressful experiences people can live through. Deciding to do both at the same time is definitely not for the fainthearted. If there's a possibility to agree on an extended settlement, this can make the scenario of buying a new house during settlement of your old house and moving from one to the other before settlement date possible. However, the possibility of not finding the right property to relocate to is always a risk.
Another thing to consider is the issues around transitioning between properties. If you buy your new home, intending to sell your existing home later, you will have to deal with the costs and stress of owning two properties for a period of time, and that could drag on for months depending on the market. However, you can then seamlessly relocate from the existing property once it's sold, straight into the new one that may have sat empty for weeks waiting for you. Alternatively, if you sell first and buy later, there may be a period in between where you'll have to find alternative accommodation as well as storage for your possessions. This can be inconvenient not to mention costly but for some is the best option, knowing they're done with one property before beginning with another. This option certainly offers a more flexible approach, given that you may find the ideal property merely weeks after settlement on your previous home. Or you could decide to take some time and wait for the market to improve from the buyer's perspective before investing again. The availability of serviced apartments, short term rentals and AirBnB properties makes this a far easier choice than it might have been in the past.
Whatever the situation you may be in, the best approach always is to do you research, know the market and get some advice from a trusted local agent to help you decide the best course of action.