Lettings markets rarely operate a sole agency system, meaning you are usually able to have more than one agent trying to find you a tenant at the same time without being penalised by higher fees. There are some localised exceptions where an agent may offer a reduced fee if you sign on a sole agency basis.
Once you have a tenant in-situ you can usually dis-instruct their managed services and re-instruct a new agent or take over the management privately should you be dissatisfied with the service level that you are receiving. You should read the terms and conditions you signed with the agent at the outset to check exactly what you have committed yourself to.
Most landlords will start by instructing one agent eight weeks before the property becomes available, then add more agents the closer the property gets to becoming vacant, and depending on the confidence levels that they have in the incumbent agent.
A lot of landlords suffer from an inertia around changing lettings agents leaving a property with the same agent that they initially instructed. Whilst there are benefits in building long term trust with a local agent, it is also clear that you should not tolerate poor performance from an agent, nor be afraid to introduce some healthy competition.
Some landlords go to the other extreme and instruct every agent in an area. Whilst this approach may feel tempting as the pressure to find a tenant mounts, it can be counter-productive. Firstly, your property can become over exposed. If a tenant sees the same property on with 10 agents they may assume that there is something wrong with the property, or even worse that they landlord is desperate. Neither is a great way to begin a negotiation.
The amount of attention you will get from your agent is also dictated by how committed you are to them. If they think that that there are 10 agents viewing this property it is likely to go to the bottom of their priority list.