We need to make a distinction between wildlife consumption and wet markets. I've been to several and although I've seen live chickens and seafood (incl. freshwater animals), I've never seen other wildlife. Mostly what is sold is fresh meat, vegetables and then other goods, certainly in conditions that would be considered unhygienic in Western Europe today. These places aren't going to cease existing, it will take time to phase them out.
Wildlife consumption is linked to Southern China. Where it happens those live animals will be purchased in wet markets. In Wuhan trading live animals was halted in early January, and nationwide in late January. The nation went into lockdown at the beginning of February. I do not
think that wet markets were closed before the lockdown, just that live animals could not be sold in them. In late February a much heralded ban on the consumption of wildlife was announced, with widespread public support.
Wet markets have now reopened, but there are lots of wrinkles here. Filming and reporting from inside them is highly restricted, so we don't know exactly what's going on (also in Wuhan they, like all stores, are operating on a sort of walk-past model; there are large barriers around them and people order from outside). I would assume that local officials, nationwide, have been given very strict instructions to make sure that the trade in wildlife does not restart in these places. I would also assume in some places it will happen anyway. Whether live domestic animals have reappeared would be an interesting question.
A complicating factor is that in February everyone in China believed the virus had originated from the wild animal market in Wuhan and there was widespread support for the permanent ceasing of such practices. Now most people in China believe that the virus was brought to Wuhan by the American military. I've not yet got a sense of whether this has impacted public opinion of wildlife consumption or not.
However, last week China announced a consultation phase on making the ban on the consumption of wildlife permanent, in effect:
新版《国家畜禽遗传资源目录》征求意见，这些动物可食用
(link in Chinese, because it's the only one I've found with the full list of exempt species)
Here are some passages, translated (by Google not me):
According to the introduction of the Ministry of Agriculture and Rural Affairs, the "Catalogue" includes a total of 31 species of domestic and traditional livestock and poultry, basically realizing that domesticated livestock and poultry should be listed. This includes:
18 kinds of traditional livestock and poultry: pigs, ordinary cattle, zebu, buffalo, yak, large cattle, sheep, goats, horses, donkeys, camels, rabbits, chickens, ducks, geese, turkeys, pigeons, quails, etc
13 species of special livestock: sika deer, red deer, reindeer, alpaca, guinea fowl, pheasant, partridge, mallard, ostrich, mink, silver fox, blue fox, raccoon dog, etc.
Notice there are several fur species included, I believe I read that the use of these animals for food will be illegal but I can't find a reference for that now.
Recently, a number of experts and scholars and representatives of the National People's Congress jointly proposed to remove the artificially cultivated terrestrial wild animals that have been included in the catalog for food purposes, re-establish the livestock genetic resources catalog, and establish a feasibility evaluation index system. According to the relevant content of the decision, it is forbidden to add the terrestrial wild animals cultivated for the purpose of food to the catalog; whether other artificially propagated wild animals can be included is subject to a rigorous evaluation and review.
If this legislation is not amended and properly implemented it will be a big step forward. However, it won't address the existing illegal trade in wildlife; presumably in fact it is going to increase it significantly. It also won't improve the welfare conditions for species that are still farmed, another key concern. There is still much to be done.
