"develop greater appreciation" is correct and usable in written English.
You can use it to express the idea that someone should become more aware of, or value, something. For example, "As we grow older, it is important to develop greater appreciation for the people and things in our lives."
A better understanding of NOS concepts assists teachers in developing greater appreciation of inquiry activities, which are less structured and more student oriented and open ended (Atar and Gallard 2011).
In 2013, Save the Children and the Frontline Health Workers Coalition created The REAL Awards, a first-of-its-kind annual global awards program designed to develop greater respect and appreciation for the lifesaving care that health workers provide in the U.S. and around the world.
That's a process that a Chicago-based organization called the Interfaith Youth Core (IFYC) has refined into something between an art and a science, demonstrating how to bring college students together across faith and belief lines so that they develop greater respect, comfort and appreciation for one another and their traditions.
Worrying not only may motivate people to take action, as in using sunscreen, but also may allow people to better prepare themselves for negative experiences in their lives and to develop a greater appreciation for positive experiences.
In Nature Rx, Donald A. Rakow and Gregory T. Eells summarize the value of nature prescription programs designed to encourage college students to spend time in nature and to develop a greater appreciation for the natural world.
You might develop a greater appreciation of just how much is possible with current technology, including how it might be used in unexpected ways in building empathy, sharing insights, sense-making, and prototyping.
