Yes, if "original frequency" refers to half of the original sampling rate, with caveats so let's review the main concepts.
Assuming the resampling is done by upsampling (zero insert), following by an interpolation FIR filter, followed by a down-sampler as follows:
Consider the spectrum after the upsampling as depicted in the figure below where the zero insert would increase the sampling rate by a factor of 8 (to $8f_s$), but also have an image at every multiple of the original sampling rate:
Without yet considering the subsequent decimation, a "perfect" interpolation filter would pass our original signal of interest with no distortion while completely eliminating the images, with a response as follows ("perfect" is not implementable, but we can trade distortion for filter complexity to get any performance we want, as long as the inevitable delay is acceptable):
To note, but not critical to this question: When our original signal doesn't occupy most of the original first Nyquist zone (out to $f_s/2$) we can (and often do) implement multi-band filters, that concentrate the rejection of the images only where needed minimizing filter resources - however we must also consider the filter's capability to reject images in the subsequent decimation process.
In this case after filtering and prior to downsampling to create the decimation process, we will have the resulting spectrum as given below, at the 8x sampling rate. After we downsample by 9 (by selecting every 9th sample), the new sampling rate (and multiples thereof) will be at the red marks indicated by $f_{s2}$ (while $f_{s1}$ refers to the original sampling rate).
Now in this case instead of having images appear at each multiple of $f_{s1}$ as we did for interpolation, we will have alias bands at each multiple of $f_{s2}$; each band occupies the same spectrum as our original signal (but two sided) and represents the frequency locations that will alias to our low pass signal.
So prior to the downsampling, we need to ensure we filter out these alias bands or it will alias in actual other signals (including the higher frequency portions of our own signal if our original sampling rate was not high enough) and/or noise which will increase the noise floor and therefore decrease SNR. As a resampling filter, we can use one filter as long as we meet both requirements for image filtering from upsampling and alias rejection for down-sampling. In this case with the higher down-sampling number, the alias rejection is more stringent and meeting that requirement will also meet the earlier requirement for image filtering. From this we can deduce as a simplistic answer that the filter's cutoff must be 8/9 of the original Nyquist boundary (half the original sampling rate), which is $4/f_{s1}/9$. But this would necessitate a brick-wall filter which is not realizable. On a practical level we must define the occupied bandwidth which must be something less than Nyquist to allow for a realizable filter transition bandwidth. Typically 70 to 80% is a reasonable occupancy but this is ultimately traded with allowable filter complexity. This is demonstrated in the graphic below showing some spectral occupancy below $f_{s2}/2$ and the resulting filter transition that this would allow. In this case our usable bandwidth is $B$, which is something less than $f_{s2}/2$ where $f_{s2}$ is 8/9 our original sampling rate of $f_{s1}$. Our filter requirement then is to pass our signal from DC to $B$ with no distortion (passband), and completely reject (to whatever rejection requirement we need) starting at $f_{s2}-B$ and above.
