One of them was an Andorian male
Female, actually. There was also Klingon male ("a friend for Worf") and humans of both genders.
^ That's good old Rick Berman for you. He thought that the makeup for Andorians (and for Tellarites as well) looked too corny - like something out of a 1950s B movie. So he refused to use them until ENT came along and the makeup department was able to convince him that they could make them look "good."
Yep. He thought they looked "hokey". But, to be fair, he was also working off a mandate made by Gene Roddenberry that races we had seen before should not be seen too often. The original premise for TNG was that the Enterprise was going to be departing known space after solving the Farpoint mystery, and therefore would not be passing through Romulan, Klingon, Andorian or Tellarite space. So, Enterprise had a token Klingon, a few Vulcans and that was going to be it for TOS races.
the one which Anwar pointed out and another one in Captain's Holiday - he's on Risa, but we only see his back during the scene where Picard is reading his book.

Holidaying Andorian on Risa by Therin of Andor, on Flickr
It's a reuse of the costume and makeup made for the Lal episode.
Um, that's silly...the Andorians were introduced in the 1960s...on TV.
With antennae that were made out of wooden cotton spools, pilfered from the seamstress's workroom.
The Andorians in TMP had slender tendrill-like antennae, made from a new type of "slip latex", then very expensive.

TMP Female by Therin of Andor, on Flickr
Similarly, the balding Andorian admiral featured in ST IV made use of state of the art latex work - on a motion picture budget - that enabled them to show off the antennae bases with no wig needed to hide the seams.

UFP Councillor, ST IV by Therin of Andor, on Flickr

Balding UFP Councillor, ST IV by Therin of Andor, on Flickr
Late 1980s TV couldn't afford that, so they had to wait till miniaturization of radio control parts enabled relatively silent movement - and then really show bang for their makeup buck!
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