It depends how far past the expiry it is, and how it's been stored. Different types of developers also degrade at different rates. Some developers will work just fine for years after their expiry date, others may be completely useless after a few months.
The first noticeable difference would be in the development time. Old developer will take longer, so you would need to experiment to figure out the required development times.
Once a developer gets completely past it though, you just won't be able to get a decent image from it, no matter how long you develop for.
If you under-develop the film because you've used an old developer and haven't compensated for this with longer development time, then there's nothing you can do about it. After fixing, you can't go back and give it another go in the developer. Your negative will be thin, and you won't be able to get decent contrast in the final print.
Having said all that, it'll either work properly or it won't. If after some experimentation you find your developer is still giving you a good image, then it's fine. You don't need to worry that it's past it's official expiry. It won't cause your negatives to degrade faster or anything like that.
To improve the lifespan of your film chemicals. You should...
- Keep them somewhere cold and dark. The colder the better, as long as it's above freezing.
- Keep air out of the containers. If you don't have one of those concertina type containers, you can just squeeze in the sides of the regular bottle, to remove as much air as possible before sealing the lid.