const regex = new RegExp(`ReGeX${testVar}ReGeX`);
...
string.replace(regex, "replacement");
Update
Per some of the comments, it's important to note that you may want to escape the variable if there is potential for malicious content (e.g. the variable comes from user input)
ES6 Update
In 2019, this would usually be written using a template string, and the above code has been updated. The original answer was:
var regex = new RegExp("ReGeX" + testVar + "ReGeX");
...
string.replace(regex, "replacement");
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