Well, sort of.

At the very least you ought to be able to LOOK like you can.

To gain muscle while losing fat is the HOLY GRAIL of bodybuilding.

Can it really, in fact, be done?

And to what extent it can be done, and for how long depends on many interesting things and on the following applicable circumstances;

1. How much calorie deficit you maintain;
2. How much protein surplus you have;
3. Your training scheme;
4. Your genetics (people gain or lose muscle, burn different ratios of fats/carbs/proteins at startlingly different rates depending upon them);
5. Your age;
6. Lifestyle characteristics (supplements, sleep, sex, drugs & rock n roll, etc.).

While it is probably not possible to gain significant amounts of muscle while simultaneously losing significant amounts of fat. It is very possible to increase the ratio of fat loss to muscle mass retained.

Back in the day, when there was a lot more trial & error and a lot less ignorant ranting theoretical hogwash on YOUTUBE, most practical competitive bodybuilders agreed there was a realistic ratio of about 75% to 25% (i.e. 3 parts fat/1 part lean tissue) as The Golden Mean and about the best you could do.

…and that, for most of us…is probably good enough.