Don't take legal advice from anyone but a lawyer that you are paying.
Seriously, this depends on a variety of factors and is especially dependent on your local laws, the specifics of the contract and most importantly, precedent.
Find a lawyer, give them your contract, detail your side project and get an opinion.
Yes. I’m in the UK and I’ve dealt with this issue more than once, including taking formal legal advice. I’m not going to add fuel to the fire by sharing exactly what happened in my specific circumstances, but this issue has subtleties and in some cases proposed contracts did get changed after the advice I received.
Seriously, if you’re talking an employment contract, or a side project with enough personal value or potential that this question is relevant, you could be talking about many thousands of pounds if things go wrong. You’d be crazy not to spend a hundred or two taking proper advice on it. A single session with any decent employment lawyer will probably be all you need — and if it isn’t, that’s even more reason not to rely on random advice from HN.