Find the cheapest renewal price you can1 and then institute a registration transfer2. It differs a bit between extensions e.g. .com is different to .co.uk which is different to .com.au.
Note the you need to pull the domain to the new registrar, not push it from the old one. So the first thing to do is create your account at the new registrar. Then get the EPP code (domain password) from the old registrar and ensure privacy is disabled and the domain is unlocked - again, not all domain extensions need this.
At the new registrar, institute a transfer in order. This is the point you will need the EPP code.
Some registrars will send an approval email which needs to be clicked for the process to proceed. Once that is done (or if it isn't needed) the transfer usually takes a few days.
The nameservers will remain unchanged.
1 Cheapest is not necessarily best, it depends on a few things.
2 Do this at least a week before it expires.