According to the text of Mantle of Majesty (a Bard College feature from the College of Glamour, Xanathar's Guide to Everything, page 14):
As a bonus action, you cast command, without expending a spell slot, and you take on an appearance of unearthly beauty for 1 minute or until your concentration ends (as if you were concentrating on a spell).
Specifically, the "as if you were concentrating on a spell" part bothers me. According to the rules, the things that can cause you to lose concentration are:
Casting another spell that requires concentration. You lose concentration on a spell if you cast another spell that requires concentration. You can’t concentrate on two Spells at once.
Taking damage. Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration. The DC equals 10 or half the damage you take, whichever number is higher. If you take damage from multiple sources, such as an arrow and a dragon’s breath, you make a separate saving throw for each source of damage.
Being incapacitated or killed. You lose concentration on a spell if you are incapacitated or if you die.
Class features are not spells. So, does this mean that if you cast a concentration spell and then use Mantle of Majesty, you can concentrate on both as long as you don't take damage?
Best Answer
No, not without breaking concentration on Mantle of Majesty
Here is clarification from Xanathar’s Guide to Everything:
Whilst Mantle of Majesty may not be a spell, it is a special ability which requires concentration, thusly casting a spell (or using another ability) that requires concentration causes your concentration to break.
The “(as if you were concentrating on a spell).” is an attempt at clarifying this.
Also, for added clarification from my own comment below this answer:
Mantle of Majesty is described as an ability: “At 6th level, you gain the ability to cloak yourself in a fey magic that makes others want to serve you.” Whilst its description doesn't use the word special ability, PHB page 45 says this about classes: “Your class gives you a variety of special features, such as a fighter's mastery of weapons and armor, and a wizard's spells.” From this we can infer that Mantle of Majesty is a special ability.