An idea of what your maximum reasonable budget is might help considerably - even at the focal length of 300mm there are $100 lenses and $1,000 lenses. Generally, the longer you go, the higher the cost - however, there are always cheaper/lower quality longer lenses and high-end expensive longer lenses. How much you can spend will help dictate how much more reach you may be able to get and at what quality level.
For example, if you have a reasonably fast 300mm lens (F4.5 or faster), then adding a good quality 1.4x teleconverter can get you a good bit more reach at a reasonable cost. But beware - if your 300mm lens is fairly slow (F6.3), it won't be able to autofocus with a teleconverter. A decent teleconverter is probably in the $150-200 range.
You can get a 500mm zoom lens for a fairly reasonable price - but the question is whether that price is within YOUR budget...used versions of the Sigma 170-500, Sigma 150-500, and Tamron 200-500, all should range in the $700-800 range U.S. - even new, some of these go for no more than $800 U.S. The quality is decent, and they have a lot more reach.
If you need to go as budget conscious as possible, you might try looking around for a used Minolta AF lens (they will work on your Sony camera). There are some inexpensive examples you might dig up that will get you more reach, with a range of quality from average to decent. They won't be 'great' but they will be quite reasonably priced. Look for the Minolta 100-400mm, the Minolta 500mm F8 mirror, the Tamron 200-400mm in Minolta/Sony mount, to name a few.