The phrase itself is highly contextual. Sometimes it's used as a high compliment for someone who is respectable and gracious:
Coach Eaves was a class act. I really admire coaches who do it right, don't go crazy on the sidelines, and set a good example for others.
(Rick Wood, 40 Seasons: The Life of a High School Basketball Coach, 2011)
Most guys would have forgotten all about a minor moment like that, but not Jimmy Stewart. He was a class act all the way.
(Tony Curtis, American Prince: A Memoir, 2008)
Sometimes it's used to describe someone's stylistic appearance, or someone who has both intelligence and charm:
She was a very serious student, both intelligent and beautiful. As they say, she was a class act. To get her attention or a smile from her was extremely hard. She had utter self-confidence, great poise, and an elegant walk.
(Vartan Gregorian, The Road to Home: My Life and Times, 2008)
Sometimes it's used to describe someone's overall classiness, in a way that sets them apart from their peers:
She was a class act. He was used to hanging around with floozies, but his taste was changing. He liked the air of eloquence that rested on her.
(Inez Brinkley, Embracing the Light, 2006)
Janelle had street sex appeal, the stark sexuality of a cocktail waitress exposing some tits and ass as she bends over to serve your drink. But this dame was a class act, a woman wrapped in pearls and sable getting out of a Rolls Royce. My first impression of her was of a cheetah with a diamond choker...
(Harold Robbins, Sin City, 2003)
In the context you mention:
The club is lucky to have such a class act...
I'd intepret that to mean that whatever act is performing wouldn't necessarily be expected to be seen in such a venue. Perhaps it's a folk singer with the voice of an angel playing in a dingy nightclub, but the expression could be used to describe a variety of circumstances.
In the setting of a club, I'd interpret a class act to be something that is more refined than raw, more sophisticated than cheesy. I would expect the performance to have broad appeal to a wide audience, as opposed to a niche act. I would expect the class act to be more stylishly dressed than other performers at the club.
Best Answer
If you are "acting in a given capacity" you are performing the function defined by the capacity, the "capacity" being a previously defined position in a society or organisation.
For example if the mayor of a town has resigned and there has not yet been an election for a new one another councillor might perform the duties of the mayor for a while without actually having the title. In that case the councillor would be "acting in the capacity of mayor".
The problem with the sentence as it stands is that the "capacity" is not very well defined. It is possible that a previous sentence has defined it well or that the writer is referring to advertising or to role models as suggested by Kate Bunting.