Alien races speak their own languages, Vulcans, Romulans "Rihannsu ", and others. Is the Klingon language the only constructed language seen on screen? If so, why did it receive more attention than any other? I am referring to constructed languages not some gibberish words made up for one time use for certain episodes.
As far as I can tell, no other language has been fully constructed for use in Star Trek, or at least not to nearly the degree that Klingon has.
Vulcan has been defined to some extent, but it seems to be less than Klingon. It is not, however, recognized as canon.
Romulan has been briefly described.
Memory Alpha lists several languages, but most seem to exist only in a few words or phrases.
So, yes it is the only fully constructed language seen on-screen.
I would like to address the part of the question: "If so, why did it receive more attention than any other?"
There was a similar question here, but I do not like the direction of the answers given here or there. I believe that only the creators and those involved with the production could answer concreately. There may be an element of luck there, but there are in my own opinion some reasons to prefer developing a language for the Klingon rather than for other species.
They are aggressive and violent so their conversations have more impact than that of a soft spoken race.
They have lots of cultural traditions which usually get separate words to specify, so a vocabulary naturally builds up. And when the vocabulary builds up faster than that for another language it stands out.
- People like to pay attention to the aggressive and violent. The OP here has the name "The Byzantine"; the Byzantine empire lasted the longest of all empires in history, and was relatively peaceful compared to other empires and ironically may be the least well known in the public. It is much less known than the Vikings for example.
And those I believe are enough to have given Klingon the advantage in being picked out for having a language developed for it.