Yes, there are a number of ways in which gender privilege manifests.
Females tend to get lighter sentencing for the same crimes, the court systems favor women massively in custody and divorce hearings, women get easier standards applied to them when seeking to become military service members, cops, firefighters, etc.
A woman can advertise as a babysitter, daycare provider, nurse or tutor and not have to worry much, if at all, that she might be dismissed as a candidate immediately upon potential clients realizing what sex she is. This is not the case for men.
Men are much more likely to experience criminal violence. Men have a massively higher suicide rate and workplace death rate. Men do all the hardest and most dangerous and least glorious jobs in our society too.
There are also, obviously, some gender privileges which men have over women. I feel that others, including the entire apparatus of our academia and media structure, are doing a fine job of exposing (and exaggerating, and lying about) these. So I won't put a lot of effort into helping that very well staffed cause.
If I were to press myself to think of a good example so I don't completely seem like I'm dismissing the male side of this (which I'm not) I'd say, for instance, men are able to be serious candidates as bodyguards and personal security whereas women are not. However, this is as it should be. Women shouldn't be considered as police, firefighters, or any sort of active combat role in the military. We are a complete clown-world society for doing any of that.
Likewise, I wouldn't for a moment deny that the imbalances I listed above which favor women over men are also rooted in realities and biology. I think some of them could maybe be alleviated a bit, or at least appreciated a bit more, but for the most part - it is that way because it must be.
Equality is a buffoonish thought to even allow to enter one's head, let alone allow to become a large scale societal goal. We are different as individuals and we are different as classes of individuals in a host of ways. Society used to pay attention to these differences, still does but lies about it, and should fully embrace doing so again.
Oh and lastly, I would agree that there are probably some ways in which we could alleviate and appreciate the imbalances which favor men over women without wrecking society even further in the process. I'd need to give it some thought. I feel we've already gone so far down that feminist / egalitarian road, the pickings are getting pretty slim when it comes to any sort of legitimate pro-female-equality thing at this point. But a few things like that may still remain.