There are hundreds of trials in various states of completion for hydroxychloroquine [1]. At least 10 of them specifically call out using it in combination with zinc, though some completed trials that don't specifically call it out in the title also used zinc if you read the papers.
There are about 35 trials in various states of completion of remdesivir [2].
If hydroxychloroquine actually does anything, we'll eventually find out. But the cold hard truth is that all the evidence so far is that remdesivir is a weakly effective treatment (shortens length of stay in hospital slightly, not a miracle cure) while hydroxychloroquine hasn't been shown to do much of anything useful in COVID. Both aren't as big a deal as Dexamethasone, which significantly reduces mortality in the sickest patients.
Most facilities have settled on using remdesivir + dexamethasone as the standard treatment for the sickest patients and have totally ditched hydroxychloroquine. Many are still administering zinc and other low-risk treatments like vitamin C and D to patients because while the evidence isn't there, there's no cost or safety reason not to try it.
The problem with talking about hydroxychloroquine is that it has become the rallying cry of the conspiracy theorist, so any talk about it results in someone saying you are "testing it wrong". The most common response is "it is a preventative treatment, not a treatment of already sick people! they are testing the wrong patients in trials!" or "it only works in combination with zinc!" or whatever. The good news is all those combinations are being trialed and if it actually does anything, we'll eventually find out. Whether anyone ever comes up with evidence that hydroxychloroquine does anything useful in COVID patients, it will definitely be one of the most studied drugs ever.
[1] https://clinicaltrials.gov/ct2/results?cond=covid&term=hydro...
[2] https://clinicaltrials.gov/ct2/results?cond=covid&term=remde...