'should be further promoted' is correct and usable in written English.
You can use it when you want to express a recommendation or to suggest that something should be encouraged, increased, or advanced. For example: "Since solar energy is so beneficial to the environment, it should be further promoted as an energy source."
On the other hand, more convenient public transportation modes in DID, such as bus, metro, and taxi, should be further promoted for older adults.
There are a number of initiatives that have been developed in Europe for increasing the teaching of radiology at undergraduate level and these should be further promoted.
This reinforced the notion that waste recycling should be further promoted in buildings, possibly through building level technological innovations and design modifications.
The procedures for evacuation planning and the need for CPAs to demonstrate and maintain the capability to effectively respond to a rare (but possibly devastating) event by carrying out regular drills and exercises should be further promoted within national programs.
Current management should therefore preferably continue in fruit tree plantations, while vegetated vineyards, which are progressively replacing conventional mineral vineyards in Valais, should be further promoted.
Thus, RDU education for both health care providers and consumers should be further promoted.
Prism was further promoted through The Prismatic World Tour.
Coordinated observation of the phenomena by multiple satellites, (e.g., the THEMIS mission, Van Allen Probes, and the Magnetospheric Multiscale (MMS) mission) and ground facilities should be promoted to further enhance the groundwork of our project (Fujimoto et al. 2012; Teramoto et al. 2016).
We should not abandon the pursuit of scientific research, if anything, it should be promoted and encouraged even further.
The Bush administration should be working to promote further offensive reductions, instead of threatening to withdraw from the ABM treaty and risk initiating a new nuclear arms race.
Providing decision makers from the municipal governments with information on policies aimed at addressing upstream determinants alongside health indicators should be encouraged further to promote knowledge on their role in addressing health inequalities.
