Should I email a Professor about a Postdoc position that they have listed on a job website?

I am currently in a Postdoc position at the University I graduated from under an advisor where I basically am in charge of a niche portion of his lab since it isn't his strongest research area. My advisor just told me to start looking for new positions since he is unsure if we will receive more funding to keep the Postdoc open.

I was looking around and found a Postdoc position under an advisor at another University that is directly in this niche area that I want to continue in. I applied to it on their website, but really want to drive home the idea that I am a great fit. Should I reach out to this new advisor over email or just wait for a response to the job posting?