Can you simulate the "response time" of a lower window size FFT on a higher window size? Can you simulate the "response time" of a lower window size FFT on a higher window size?

That is, is it possible to calculate the equivalent lower window sized FFTs from a higher one in order to iterate over the equivalent e.g. 128 window sized FFTs, but plot the higher one e.g. 8192 samples window size?

This is a problem in e.g. when one is sampling at a higher window size for the FFT, but some signal parts (e.g. strong amplitude peaks in audio) appear at a faster pace and are thus "missed" by the FFT. Or not necessarily the FFT, but any processing that uses that higher window size FFT.

What I therefore need is the visible resolution of a higher window size and the faster response of a lower window size.

My application (in audio) requires me to be able to track frequencies that follow closely to the beats of the audio. If e.g. a drum loop plays at a high bpm, then a 8192 samples FFT might be too slow to be done reading form since it changes slower than the drum loop's frequencies.
No. The time of accumulation will determine the resolution of frequencies - how far are measures separated.