Dragon Age, will receive a similar remaster.
To compare BioWare's two franchises is a difficult matter, as both were made at different times with different teams. One important factor of Mass Effect Legendary Edition's release is that it came only after Mass Effect: Andromeda had launched. The newest entry in the ME franchise left much to be desired and was graced with several much-needed patches before the studio was able to move on. It stands to reason that Dragon Age will follow a similar pattern before the series receives a remaster.
Dragon Age 4 was initially announced back in 2018 and has experienced several setbacks. More difficulties for the project came with the left to Ubisoft. Presently, Dragon Age 4 has yet to announce a dedicated release date, save for the announcement that it will release April 2022 at the earliest. If Dragon Age is following Mass Effect's pattern, it can be assumed that a Dragon Age remaster is a few years out at least.
Mass Effect & Dragon Age: Different Game, Different Story
Another barrier to a potential remaster for the Dragon Age series would be its latest installment's place in game consoles. Dragon Age Inquisition was released back in 2014 on Xbox One and Xbox 360, but its graphics and gameplay have held up better than most games released during that time. Despite the difficulty in remastering Dragon Age Inquisition, there is another entry in the franchise that is more overdue for a remaster. Widely hailed as a masterpiece, Dragon Age Origins was the game that kicked off the franchise into the fantasy legacy it has today. DAO was initially released in 2009 and has set the precedent for many RPGs since.
Mass Effect and Dragon Age both tackled their stories very differently. While Mass Effect enjoyed the luxury of a set cast of characters that could be expanded with each game, as well as a recurring protagonist, Dragon Age introduces a new cast with each installment. Marketing the original Mass Effect trilogy together makes perfect sense, as it encomes the adventures of Commander Shepard throughout the Reaper War. BioWare would need to examine whether it would benefit from another remastered trilogy, despite the disconnected stories and cast, or choose to remaster a single installment from the franchise.
While the very idea of a Dragon Age remaster is likely far away, work continues on Dragon Age 4. Given the success of the Mass Effect Legendary Edition remaster, it stands to reason that this is a project BioWare will consider pursuing in the future after the fourth installment has been completed and released. There is currently no announcement for Dragon Age 4's release date, and there is no news on other projects in the Dragon Age universe.